Daily Papers

Recently, partial Bayesian neural networks (pBNNs), which only consider a subset of the parameters to be stochastic, were shown to perform competitively with full Bayesian neural networks. However, pBNNs are often multi-modal in the latent-variable space and thus challenging to approximate with parametric models. To address this problem, we propose an efficient sampling-based training strategy, wherein the training of a pBNN is formulated as simulating a Feynman--Kac model. We then describe variations of sequential Monte Carlo samplers that allow us to simultaneously estimate the parameters and the latent posterior distribution of this model at a tractable computational cost. We show on various synthetic and real-world datasets that our proposed training scheme outperforms the state of the art in terms of predictive performance.

Stochastic latent variable models (LVMs) achieve state-of-the-art performance on natural image generation but are still inferior to deterministic models on speech. In this paper, we develop a speech benchmark of popular temporal LVMs and compare them against state-of-the-art deterministic models. We report the likelihood, which is a much used metric in the image domain, but rarely, or incomparably, reported for speech models. To assess the quality of the learned representations, we also compare their usefulness for phoneme recognition. Finally, we adapt the Clockwork VAE, a state-of-the-art temporal LVM for video generation, to the speech domain. Despite being autoregressive only in latent space, we find that the Clockwork VAE can outperform previous LVMs and reduce the gap to deterministic models by using a hierarchy of latent variables.

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper proposes a new generative model, a dynamic version of the log-linear topic model of~mnih2007three. The methodological novelty is to use the prior to compute closed form expressions for word statistics. This provides a theoretical justification for nonlinear models like PMI, word2vec, and GloVe, as well as some hyperparameter choices. It also helps explain why low-dimensional semantic embeddings contain linear algebraic structure that allows solution of word analogies, as shown by~mikolov2013efficient and many subsequent papers. Experimental support is provided for the generative model assumptions, the most important of which is that latent word vectors are fairly uniformly dispersed in space.

We propose the Distance-informed Neural Process (DNP), a novel variant of Neural Processes that improves uncertainty estimation by combining global and distance-aware local latent structures. Standard Neural Processes (NPs) often rely on a global latent variable and struggle with uncertainty calibration and capturing local data dependencies. DNP addresses these limitations by introducing a global latent variable to model task-level variations and a local latent variable to capture input similarity within a distance-preserving latent space. This is achieved through bi-Lipschitz regularization, which bounds distortions in input relationships and encourages the preservation of relative distances in the latent space. This modeling approach allows DNP to produce better-calibrated uncertainty estimates and more effectively distinguish in- from out-of-distribution data. Empirical results demonstrate that DNP achieves strong predictive performance and improved uncertainty calibration across regression and classification tasks.

Variational Autoencoders (VAEs) have become a cornerstone in generative modeling and representation learning within machine learning. This paper explores a nuanced aspect of VAEs, focusing on interpreting the Kullback-Leibler (KL) Divergence, a critical component within the Evidence Lower Bound (ELBO) that governs the trade-off between reconstruction accuracy and regularization. Meanwhile, the KL Divergence enforces alignment between latent variable distributions and a prior imposing a structure on the overall latent space but leaves individual variable distributions unconstrained. The proposed method redefines the ELBO with a mixture of Gaussians for the posterior probability, introduces a regularization term to prevent variance collapse, and employs a PatchGAN discriminator to enhance texture realism. Implementation details involve ResNetV2 architectures for both the Encoder and Decoder. The experiments demonstrate the ability to generate realistic faces, offering a promising solution for enhancing VAE-based generative models.

Large, text-conditioned generative diffusion models have recently gained a lot of attention for their impressive performance in generating high-fidelity images from text alone. However, achieving high-quality results is almost unfeasible in a one-shot fashion. On the contrary, text-guided image generation involves the user making many slight changes to inputs in order to iteratively carve out the envisioned image. However, slight changes to the input prompt often lead to entirely different images being generated, and thus the control of the artist is limited in its granularity. To provide flexibility, we present the Stable Artist, an image editing approach enabling fine-grained control of the image generation process. The main component is semantic guidance (SEGA) which steers the diffusion process along variable numbers of semantic directions. This allows for subtle edits to images, changes in composition and style, as well as optimization of the overall artistic conception. Furthermore, SEGA enables probing of latent spaces to gain insights into the representation of concepts learned by the model, even complex ones such as 'carbon emission'. We demonstrate the Stable Artist on several tasks, showcasing high-quality image editing and composition.

This paper addresses the challenge of text-conditioned streaming motion generation, which requires us to predict the next-step human pose based on variable-length historical motions and incoming texts. Existing methods struggle to achieve streaming motion generation, e.g., diffusion models are constrained by pre-defined motion lengths, while GPT-based methods suffer from delayed response and error accumulation problem due to discretized non-causal tokenization. To solve these problems, we propose MotionStreamer, a novel framework that incorporates a continuous causal latent space into a probabilistic autoregressive model. The continuous latents mitigate information loss caused by discretization and effectively reduce error accumulation during long-term autoregressive generation. In addition, by establishing temporal causal dependencies between current and historical motion latents, our model fully utilizes the available information to achieve accurate online motion decoding. Experiments show that our method outperforms existing approaches while offering more applications, including multi-round generation, long-term generation, and dynamic motion composition. Project Page: https://zju3dv.github.io/MotionStreamer/

Transformers are the dominant architecture for sequence modeling, but there is growing interest in models that use a fixed-size latent state that does not depend on the sequence length, which we refer to as "generalized state space models" (GSSMs). In this paper we show that while GSSMs are promising in terms of inference-time efficiency, they are limited compared to transformer models on tasks that require copying from the input context. We start with a theoretical analysis of the simple task of string copying and prove that a two layer transformer can copy strings of exponential length while GSSMs are fundamentally limited by their fixed-size latent state. Empirically, we find that transformers outperform GSSMs in terms of efficiency and generalization on synthetic tasks that require copying the context. Finally, we evaluate pretrained large language models and find that transformer models dramatically outperform state space models at copying and retrieving information from context. Taken together, these results suggest a fundamental gap between transformers and GSSMs on tasks of practical interest.

We propose SketchINR, to advance the representation of vector sketches with implicit neural models. A variable length vector sketch is compressed into a latent space of fixed dimension that implicitly encodes the underlying shape as a function of time and strokes. The learned function predicts the xy point coordinates in a sketch at each time and stroke. Despite its simplicity, SketchINR outperforms existing representations at multiple tasks: (i) Encoding an entire sketch dataset into a fixed size latent vector, SketchINR gives 60times and 10times data compression over raster and vector sketches, respectively. (ii) SketchINR's auto-decoder provides a much higher-fidelity representation than other learned vector sketch representations, and is uniquely able to scale to complex vector sketches such as FS-COCO. (iii) SketchINR supports parallelisation that can decode/render sim100times faster than other learned vector representations such as SketchRNN. (iv) SketchINR, for the first time, emulates the human ability to reproduce a sketch with varying abstraction in terms of number and complexity of strokes. As a first look at implicit sketches, SketchINR's compact high-fidelity representation will support future work in modelling long and complex sketches.

Most speech recognition tasks pertain to mapping words across two modalities: acoustic and orthographic. In this work, we suggest learning encoders that map variable-length, acoustic or phonetic, sequences that represent words into fixed-dimensional vectors in a shared latent space; such that the distance between two word vectors represents how closely the two words sound. Instead of directly learning the distances between word vectors, we employ weak supervision and model a binary classification task to predict whether two inputs, one of each modality, represent the same word given a distance threshold. We explore various deep-learning models, bimodal contrastive losses, and techniques for mining hard negative examples such as the semi-supervised technique of self-labeling. Our best model achieves an F_1 score of 0.95 for the binary classification task.

Current auto-regressive mesh generation methods suffer from issues such as incompleteness, insufficient detail, and poor generalization. In this paper, we propose an Auto-regressive Auto-encoder (ArAE) model capable of generating high-quality 3D meshes with up to 4,000 faces at a spatial resolution of 512^3. We introduce a novel mesh tokenization algorithm that efficiently compresses triangular meshes into 1D token sequences, significantly enhancing training efficiency. Furthermore, our model compresses variable-length triangular meshes into a fixed-length latent space, enabling training latent diffusion models for better generalization. Extensive experiments demonstrate the superior quality, diversity, and generalization capabilities of our model in both point cloud and image-conditioned mesh generation tasks.

The increasing frequency of extreme weather events due to global climate change urges accurate weather prediction. Recently, great advances have been made by the end-to-end methods, thanks to deep learning techniques, but they face limitations of representation inconsistency in multivariable integration and struggle to effectively capture the dependency between variables, which is required in complex weather systems. Treating different variables as distinct modalities and applying a two-stage training approach from multimodal models can partially alleviate this issue, but due to the inconformity in training tasks between the two stages, the results are often suboptimal. To address these challenges, we propose an implicit two-stage training method, configuring separate encoders and decoders for each variable. In detailed, in the first stage, the Translator is frozen while the Encoders and Decoders learn a shared latent space, in the second stage, the Encoders and Decoders are frozen, and the Translator captures inter-variable interactions for prediction. Besides, by introducing a self-attention mechanism for multivariable fusion in the latent space, the performance achieves further improvements. Empirically, extensive experiments show the state-of-the-art performance of our method. Specifically, it reduces the MSE for near-surface air temperature and relative humidity predictions by 28.82\% and 23.39\%, respectively. The source code is available at https://github.com/ShremG/Met2Net.

Latent variable generative models have emerged as powerful tools for generative tasks including image and video synthesis. These models are enabled by pretrained autoencoders that map high resolution data into a compressed lower dimensional latent space, where the generative models can subsequently be developed while requiring fewer computational resources. Despite their effectiveness, the direct application of latent variable models to higher dimensional domains such as videos continues to pose challenges for efficient training and inference. In this paper, we propose an autoencoder that projects volumetric data onto a four-plane factorized latent space that grows sublinearly with the input size, making it ideal for higher dimensional data like videos. The design of our factorized model supports straightforward adoption in a number of conditional generation tasks with latent diffusion models (LDMs), such as class-conditional generation, frame prediction, and video interpolation. Our results show that the proposed four-plane latent space retains a rich representation needed for high-fidelity reconstructions despite the heavy compression, while simultaneously enabling LDMs to operate with significant improvements in speed and memory.

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

Identifying low-dimensional latent structures within high-dimensional data has long been a central topic in the machine learning community, driven by the need for data compression, storage, transmission, and deeper data understanding. Traditional methods, such as principal component analysis (PCA) and autoencoders (AE), operate in an unsupervised manner, ignoring label information even when it is available. In this work, we introduce a unified method capable of learning latent spaces in both unsupervised and supervised settings. We formulate the problem as a nonlinear multiple-response regression within an index model context. By applying the generalized Stein's lemma, the latent space can be estimated without knowing the nonlinear link functions. Our method can be viewed as a nonlinear generalization of PCA. Moreover, unlike AE and other neural network methods that operate as "black boxes", our approach not only offers better interpretability but also reduces computational complexity while providing strong theoretical guarantees. Comprehensive numerical experiments and real data analyses demonstrate the superior performance of our method.

Joint Embedding Predictive Architectures (JEPA) have emerged as a powerful framework for learning general-purpose representations. However, these models often lack interpretability and suffer from inefficiencies due to dense embedding representations. We propose SparseJEPA, an extension that integrates sparse representation learning into the JEPA framework to enhance the quality of learned representations. SparseJEPA employs a penalty method that encourages latent space variables to be shared among data features with strong semantic relationships, while maintaining predictive performance. We demonstrate the effectiveness of SparseJEPA by training on the CIFAR-100 dataset and pre-training a lightweight Vision Transformer. The improved embeddings are utilized in linear-probe transfer learning for both image classification and low-level tasks, showcasing the architecture's versatility across different transfer tasks. Furthermore, we provide a theoretical proof that demonstrates that the grouping mechanism enhances representation quality. This was done by displaying that grouping reduces Multiinformation among latent-variables, including proofing the Data Processing Inequality for Multiinformation. Our results indicate that incorporating sparsity not only refines the latent space but also facilitates the learning of more meaningful and interpretable representations. In further work, hope to further extend this method by finding new ways to leverage the grouping mechanism through object-centric representation learning.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

The field of Text-to-Speech has experienced huge improvements last years benefiting from deep learning techniques. Producing realistic speech becomes possible now. As a consequence, the research on the control of the expressiveness, allowing to generate speech in different styles or manners, has attracted increasing attention lately. Systems able to control style have been developed and show impressive results. However the control parameters often consist of latent variables and remain complex to interpret. In this paper, we analyze and compare different latent spaces and obtain an interpretation of their influence on expressive speech. This will enable the possibility to build controllable speech synthesis systems with an understandable behaviour.

This paper proposes a methodology for discovering meaningful properties in data by exploring the latent space of unsupervised deep generative models. We combine manipulation of individual latent variables to extreme values with methods inspired by causal inference into an approach we call causal disentanglement with extreme values (CDEV) and show that this method yields insights for model interpretability. With this, we can test for what properties of unknown data the model encodes as meaningful, using it to glean insight into the communication system of sperm whales (Physeter macrocephalus), one of the most intriguing and understudied animal communication systems. The network architecture used has been shown to learn meaningful representations of speech; here, it is used as a learning mechanism to decipher the properties of another vocal communication system in which case we have no ground truth. The proposed methodology suggests that sperm whales encode information using the number of clicks in a sequence, the regularity of their timing, and audio properties such as the spectral mean and the acoustic regularity of the sequences. Some of these findings are consistent with existing hypotheses, while others are proposed for the first time. We also argue that our models uncover rules that govern the structure of units in the communication system and apply them while generating innovative data not shown during training. This paper suggests that an interpretation of the outputs of deep neural networks with causal inference methodology can be a viable strategy for approaching data about which little is known and presents another case of how deep learning can limit the hypothesis space. Finally, the proposed approach can be extended to other architectures and datasets.

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models fall short in learning sequence data with sharp transitions - common in many real-world systems - due to numerical challenges during optimization. In this work, we propose LS4, a generative model for sequences with latent variables evolving according to a state space ODE to increase modeling capacity. Inspired by recent deep state space models (S4), we achieve speedups by leveraging a convolutional representation of LS4 which bypasses the explicit evaluation of hidden states. We show that LS4 significantly outperforms previous continuous-time generative models in terms of marginal distribution, classification, and prediction scores on real-world datasets in the Monash Forecasting Repository, and is capable of modeling highly stochastic data with sharp temporal transitions. LS4 sets state-of-the-art for continuous-time latent generative models, with significant improvement of mean squared error and tighter variational lower bounds on irregularly-sampled datasets, while also being x100 faster than other baselines on long sequences.

This paper presents a novel generative framework for learning shared latent representations across multimodal data. Many advanced multimodal methods focus on capturing all combinations of modality-specific details across inputs, which can inadvertently obscure the high-level semantic concepts that are shared across modalities. Notably, Multimodal VAEs with low-dimensional latent variables are designed to capture shared representations, enabling various tasks such as joint multimodal synthesis and cross-modal inference. However, multimodal VAEs often struggle to design expressive joint variational posteriors and suffer from low-quality synthesis. In this work, ShaLa addresses these challenges by integrating a novel architectural inference model and a second-stage expressive diffusion prior, which not only facilitates effective inference of shared latent representation but also significantly improves the quality of downstream multimodal synthesis. We validate ShaLa extensively across multiple benchmarks, demonstrating superior coherence and synthesis quality compared to state-of-the-art multimodal VAEs. Furthermore, ShaLa scales to many more modalities while prior multimodal VAEs have fallen short in capturing the increasing complexity of the shared latent space.

Normalizing flow models have been used successfully for generative image super-resolution (SR) by approximating complex distribution of natural images to simple tractable distribution in latent space through Invertible Neural Networks (INN). These models can generate multiple realistic SR images from one low-resolution (LR) input using randomly sampled points in the latent space, simulating the ill-posed nature of image upscaling where multiple high-resolution (HR) images correspond to the same LR. Lately, the invertible process in INN has also been used successfully by bidirectional image rescaling models like IRN and HCFlow for joint optimization of downscaling and inverse upscaling, resulting in significant improvements in upscaled image quality. While they are optimized for image downscaling too, the ill-posed nature of image downscaling, where one HR image could be downsized to multiple LR images depending on different interpolation kernels and resampling methods, is not considered. A new downscaling latent variable, in addition to the original one representing uncertainties in image upscaling, is introduced to model variations in the image downscaling process. This dual latent variable enhancement is applicable to different image rescaling models and it is shown in extensive experiments that it can improve image upscaling accuracy consistently without sacrificing image quality in downscaled LR images. It is also shown to be effective in enhancing other INN-based models for image restoration applications like image hiding.

The discovery of the disentanglement properties of the latent space in GANs motivated a lot of research to find the semantically meaningful directions on it. In this paper, we suggest that the disentanglement property is closely related to the geometry of the latent space. In this regard, we propose an unsupervised method for finding the semantic-factorizing directions on the intermediate latent space of GANs based on the local geometry. Intuitively, our proposed method, called Local Basis, finds the principal variation of the latent space in the neighborhood of the base latent variable. Experimental results show that the local principal variation corresponds to the semantic factorization and traversing along it provides strong robustness to image traversal. Moreover, we suggest an explanation for the limited success in finding the global traversal directions in the latent space, especially W-space of StyleGAN2. We show that W-space is warped globally by comparing the local geometry, discovered from Local Basis, through the metric on Grassmannian Manifold. The global warpage implies that the latent space is not well-aligned globally and therefore the global traversal directions are bound to show limited success on it.

Latent-based image generative models, such as Latent Diffusion Models (LDMs) and Mask Image Models (MIMs), have achieved notable success in image generation tasks. These models typically leverage reconstructive autoencoders like VQGAN or VAE to encode pixels into a more compact latent space and learn the data distribution in the latent space instead of directly from pixels. However, this practice raises a pertinent question: Is it truly the optimal choice? In response, we begin with an intriguing observation: despite sharing the same latent space, autoregressive models significantly lag behind LDMs and MIMs in image generation. This finding contrasts sharply with the field of NLP, where the autoregressive model GPT has established a commanding presence. To address this discrepancy, we introduce a unified perspective on the relationship between latent space and generative models, emphasizing the stability of latent space in image generative modeling. Furthermore, we propose a simple but effective discrete image tokenizer to stabilize the latent space for image generative modeling. Experimental results show that image autoregressive modeling with our tokenizer (DiGIT) benefits both image understanding and image generation with the next token prediction principle, which is inherently straightforward for GPT models but challenging for other generative models. Remarkably, for the first time, a GPT-style autoregressive model for images outperforms LDMs, which also exhibits substantial improvement akin to GPT when scaling up model size. Our findings underscore the potential of an optimized latent space and the integration of discrete tokenization in advancing the capabilities of image generative models. The code is available at https://github.com/DAMO-NLP-SG/DiGIT.

Multi-modal data-sets are ubiquitous in modern applications, and multi-modal Variational Autoencoders are a popular family of models that aim to learn a joint representation of the different modalities. However, existing approaches suffer from a coherence-quality tradeoff, where models with good generation quality lack generative coherence across modalities, and vice versa. We discuss the limitations underlying the unsatisfactory performance of existing methods, to motivate the need for a different approach. We propose a novel method that uses a set of independently trained, uni-modal, deterministic autoencoders. Individual latent variables are concatenated into a common latent space, which is fed to a masked diffusion model to enable generative modeling. We also introduce a new multi-time training method to learn the conditional score network for multi-modal diffusion. Our methodology substantially outperforms competitors in both generation quality and coherence, as shown through an extensive experimental campaign.

Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).

In open-domain dialogue generation tasks, contexts and responses in most datasets are one-to-one mapped, violating an important many-to-many characteristic: a context leads to various responses, and a response answers multiple contexts. Without such patterns, models poorly generalize and prefer responding safely. Many attempts have been made in either multi-turn settings from a one-to-many perspective or in a many-to-many perspective but limited to single-turn settings. The major challenge to many-to-many augment multi-turn dialogues is that discretely replacing each turn with semantic similarity breaks fragile context coherence. In this paper, we propose DialoGue Path Sampling (DialoGPS) method in continuous semantic space, the first many-to-many augmentation method for multi-turn dialogues. Specifically, we map a dialogue to our extended Brownian Bridge, a special Gaussian process. We sample latent variables to form coherent dialogue paths in the continuous space. A dialogue path corresponds to a new multi-turn dialogue and is used as augmented training data. We show the effect of DialoGPS with both automatic and human evaluation.

We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts, which can lead to suboptimal performance. To address this limitation, we introduce a method for prompt tuning, which jointly optimizes the text embedding on-the-fly while running the reverse diffusion process. This allows us to generate images that are more faithful to the diffusion prior. In addition, we propose a method to keep the evolution of latent variables within the range space of the encoder, by projection. This helps to reduce image artifacts, a major problem when using latent diffusion models instead of pixel-based diffusion models. Our combined method, called P2L, outperforms both image- and latent-diffusion model-based inverse problem solvers on a variety of tasks, such as super-resolution, deblurring, and inpainting.

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping from its latent space to image space. To tackle this problem, we present Isometric Diffusion, equipping a diffusion model with a geometric regularizer to guide the model to learn a geometrically sound latent space of the training data manifold. This approach allows diffusion models to learn a more disentangled latent space, which enables smoother interpolation, more accurate inversion, and more precise control over attributes directly in the latent space. Our extensive experiments consisting of image interpolations, image inversions, and linear editing show the effectiveness of our method.

Characterizing the relationship between neural population activity and behavioral data is a central goal of neuroscience. While latent variable models (LVMs) are successful in describing high-dimensional time-series data, they are typically only designed for a single type of data, making it difficult to identify structure shared across different experimental data modalities. Here, we address this shortcoming by proposing an unsupervised LVM which extracts temporally evolving shared and independent latents for distinct, simultaneously recorded experimental modalities. We do this by combining Gaussian Process Factor Analysis (GPFA), an interpretable LVM for neural spiking data with temporally smooth latent space, with Gaussian Process Variational Autoencoders (GP-VAEs), which similarly use a GP prior to characterize correlations in a latent space, but admit rich expressivity due to a deep neural network mapping to observations. We achieve interpretability in our model by partitioning latent variability into components that are either shared between or independent to each modality. We parameterize the latents of our model in the Fourier domain, and show improved latent identification using this approach over standard GP-VAE methods. We validate our model on simulated multi-modal data consisting of Poisson spike counts and MNIST images that scale and rotate smoothly over time. We show that the multi-modal GP-VAE (MM-GPVAE) is able to not only identify the shared and independent latent structure across modalities accurately, but provides good reconstructions of both images and neural rates on held-out trials. Finally, we demonstrate our framework on two real world multi-modal experimental settings: Drosophila whole-brain calcium imaging alongside tracked limb positions, and Manduca sexta spike train measurements from ten wing muscles as the animal tracks a visual stimulus.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

Generative models serve as powerful tools for modeling the real world, with mainstream diffusion models, particularly those based on the latent diffusion model paradigm, achieving remarkable progress across various tasks, such as image and video synthesis. Latent diffusion models are typically trained using Variational Autoencoders (VAEs), interacting with VAE latents rather than the real samples. While this generative paradigm speeds up training and inference, the quality of the generated outputs is limited by the latents' quality. Traditional VAE latents are often seen as spatial compression in pixel space and lack explicit semantic representations, which are essential for modeling the real world. In this paper, we introduce ReaLS (Representation-Aligned Latent Space), which integrates semantic priors to improve generation performance. Extensive experiments show that fundamental DiT and SiT trained on ReaLS can achieve a 15% improvement in FID metric. Furthermore, the enhanced semantic latent space enables more perceptual downstream tasks, such as segmentation and depth estimation.

Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.

Generative modeling of crystal data distribution is an important yet challenging task due to the unique periodic physical symmetry of crystals. Diffusion-based methods have shown early promise in modeling crystal distribution. More recently, Bayesian Flow Networks were introduced to aggregate noisy latent variables, resulting in a variance-reduced parameter space that has been shown to be advantageous for modeling Euclidean data distributions with structural constraints (Song et al., 2023). Inspired by this, we seek to unlock its potential for modeling variables located in non-Euclidean manifolds e.g. those within crystal structures, by overcoming challenging theoretical issues. We introduce CrysBFN, a novel crystal generation method by proposing a periodic Bayesian flow, which essentially differs from the original Gaussian-based BFN by exhibiting non-monotonic entropy dynamics. To successfully realize the concept of periodic Bayesian flow, CrysBFN integrates a new entropy conditioning mechanism and empirically demonstrates its significance compared to time-conditioning. Extensive experiments over both crystal ab initio generation and crystal structure prediction tasks demonstrate the superiority of CrysBFN, which consistently achieves new state-of-the-art on all benchmarks. Surprisingly, we found that CrysBFN enjoys a significant improvement in sampling efficiency, e.g., ~100x speedup 10 v.s. 2000 steps network forwards) compared with previous diffusion-based methods on MP-20 dataset. Code is available at https://github.com/wu-han-lin/CrysBFN.

Recent works have shown that generative data augmentation, where synthetic samples generated from deep generative models complement the training dataset, benefit NLP tasks. In this work, we extend this approach to the task of dialog state tracking for goal-oriented dialogs. Due to the inherent hierarchical structure of goal-oriented dialogs over utterances and related annotations, the deep generative model must be capable of capturing the coherence among different hierarchies and types of dialog features. We propose the Variational Hierarchical Dialog Autoencoder (VHDA) for modeling the complete aspects of goal-oriented dialogs, including linguistic features and underlying structured annotations, namely speaker information, dialog acts, and goals. The proposed architecture is designed to model each aspect of goal-oriented dialogs using inter-connected latent variables and learns to generate coherent goal-oriented dialogs from the latent spaces. To overcome training issues that arise from training complex variational models, we propose appropriate training strategies. Experiments on various dialog datasets show that our model improves the downstream dialog trackers' robustness via generative data augmentation. We also discover additional benefits of our unified approach to modeling goal-oriented dialogs: dialog response generation and user simulation, where our model outperforms previous strong baselines.

The variational autoencoder (VAE) is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other DLVMs. The bottleneck dimension of the VAE is a crucial design choice, and it has strong ramifications for the model's performance, such as finding the hidden explanatory factors of a dataset using the representations learned by the VAE. However, the size of the latent dimension of the VAE is often treated as a hyperparameter estimated empirically through trial and error. To this end, we propose a statistical formulation to discover the relevant latent factors required for modeling a dataset. In this work, we use a hierarchical prior in the latent space that estimates the variance of the latent axes using the encoded data, which identifies the relevant latent dimensions. For this, we replace the fixed prior in the VAE objective function with a hierarchical prior, keeping the remainder of the formulation unchanged. We call the proposed method the automatic relevancy detection in the variational autoencoder (ARD-VAE). We demonstrate the efficacy of the ARD-VAE on multiple benchmark datasets in finding the relevant latent dimensions and their effect on different evaluation metrics, such as FID score and disentanglement analysis.

Recent advances in latent diffusion models have demonstrated their effectiveness for high-resolution image synthesis. However, the properties of the latent space from tokenizer for better learning and generation of diffusion models remain under-explored. Theoretically and empirically, we find that improved generation quality is closely tied to the latent distributions with better structure, such as the ones with fewer Gaussian Mixture modes and more discriminative features. Motivated by these insights, we propose MAETok, an autoencoder (AE) leveraging mask modeling to learn semantically rich latent space while maintaining reconstruction fidelity. Extensive experiments validate our analysis, demonstrating that the variational form of autoencoders is not necessary, and a discriminative latent space from AE alone enables state-of-the-art performance on ImageNet generation using only 128 tokens. MAETok achieves significant practical improvements, enabling a gFID of 1.69 with 76x faster training and 31x higher inference throughput for 512x512 generation. Our findings show that the structure of the latent space, rather than variational constraints, is crucial for effective diffusion models. Code and trained models are released.

Lung cancer is responsible for 21% of cancer deaths in the UK and five-year survival rates are heavily influenced by the stage the cancer was identified at. Recent studies have demonstrated the capability of AI methods for accurate and early diagnosis of lung cancer from routine scans. However, this evidence has not translated into clinical practice with one barrier being a lack of interpretable models. This study investigates the application Variational Autoencoders (VAEs), a type of generative AI model, to lung cancer lesions. Proposed models were trained on lesions extracted from 3D CT scans in the LIDC-IDRI public dataset. Latent vector representations of 2D slices produced by the VAEs were explored through clustering to justify their quality and used in an MLP classifier model for lung cancer diagnosis, the best model achieved state-of-the-art metrics of AUC 0.98 and 93.1% accuracy. Cluster analysis shows the VAE latent space separates the dataset of malignant and benign lesions based on meaningful feature components including tumour size, shape, patient and malignancy class. We also include a comparative analysis of the standard Gaussian VAE (GVAE) and the more recent Dirichlet VAE (DirVAE), which replaces the prior with a Dirichlet distribution to encourage a more explainable latent space with disentangled feature representation. Finally, we demonstrate the potential for latent space traversals corresponding to clinically meaningful feature changes.

Latent variable models (LVMs) with discrete compositional latents are an important but challenging setting due to a combinatorially large number of possible configurations of the latents. A key tradeoff in modeling the posteriors over latents is between expressivity and tractable optimization. For algorithms based on expectation-maximization (EM), the E-step is often intractable without restrictive approximations to the posterior. We propose the use of GFlowNets, algorithms for sampling from an unnormalized density by learning a stochastic policy for sequential construction of samples, for this intractable E-step. By training GFlowNets to sample from the posterior over latents, we take advantage of their strengths as amortized variational inference algorithms for complex distributions over discrete structures. Our approach, GFlowNet-EM, enables the training of expressive LVMs with discrete compositional latents, as shown by experiments on non-context-free grammar induction and on images using discrete variational autoencoders (VAEs) without conditional independence enforced in the encoder.

Despite the groundbreaking success of diffusion models in generating high-fidelity images, their latent space remains relatively under-explored, even though it holds significant promise for enabling versatile and interpretable image editing capabilities. The complicated denoising trajectory and high dimensionality of the latent space make it extremely challenging to interpret. Existing methods mainly explore the feature space of U-Net in Diffusion Models (DMs) instead of the latent space itself. In contrast, we directly investigate the latent space via Singular Value Decomposition (SVD) and discover three useful properties that can be used to control generation results without the requirements of data collection and maintain identity fidelity generated images. Based on these properties, we propose a novel image editing framework that is capable of learning arbitrary attributes from one pair of latent codes destined by text prompts in Stable Diffusion Models. To validate our approach, extensive experiments are conducted to demonstrate its effectiveness and flexibility in image editing. We will release our codes soon to foster further research and applications in this area.

The use of autoencoders for shape editing or generation through latent space manipulation suffers from unpredictable changes in the output shape. Our autoencoder-based method enables intuitive shape editing in latent space by disentangling latent sub-spaces into style variables and control points on the surface that can be manipulated independently. The key idea is adding a Lipschitz-type constraint to the loss function, i.e. bounding the change of the output shape proportionally to the change in latent space, leading to interpretable latent space representations. The control points on the surface that are part of the latent code of an object can then be freely moved, allowing for intuitive shape editing directly in latent space. We evaluate our method by comparing to state-of-the-art data-driven shape editing methods. We further demonstrate the expressiveness of our learned latent space by leveraging it for unsupervised part segmentation.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Diffusion models have achieved unprecedented performance in generative modeling. The commonly-adopted formulation of the latent code of diffusion models is a sequence of gradually denoised samples, as opposed to the simpler (e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper provides an alternative, Gaussian formulation of the latent space of various diffusion models, as well as an invertible DPM-Encoder that maps images into the latent space. While our formulation is purely based on the definition of diffusion models, we demonstrate several intriguing consequences. (1) Empirically, we observe that a common latent space emerges from two diffusion models trained independently on related domains. In light of this finding, we propose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image translation. Furthermore, applying CycleDiffusion to text-to-image diffusion models, we show that large-scale text-to-image diffusion models can be used as zero-shot image-to-image editors. (2) One can guide pre-trained diffusion models and GANs by controlling the latent codes in a unified, plug-and-play formulation based on energy-based models. Using the CLIP model and a face recognition model as guidance, we demonstrate that diffusion models have better coverage of low-density sub-populations and individuals than GANs. The code is publicly available at https://github.com/ChenWu98/cycle-diffusion.

Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets which clearly show the superiority of the discrete latent space and obtain state of the art graph generative performance, making GLAD the first latent space graph generative model with competitive performance. Our source code is published at: https://github.com/v18nguye/GLAD.

Text-guided diffusion models (TDMs) are widely applied but can fail unexpectedly. Common failures include: (i) natural-looking text prompts generating images with the wrong content, or (ii) different random samples of the latent variables that generate vastly different, and even unrelated, outputs despite being conditioned on the same text prompt. In this work, we aim to study and understand the failure modes of TDMs in more detail. To achieve this, we propose SAGE, the first adversarial search method on TDMs that systematically explores the discrete prompt space and the high-dimensional latent space, to automatically discover undesirable behaviors and failure cases in image generation. We use image classifiers as surrogate loss functions during searching, and employ human inspections to validate the identified failures. For the first time, our method enables efficient exploration of both the discrete and intricate human language space and the challenging latent space, overcoming the gradient vanishing problem. Then, we demonstrate the effectiveness of SAGE on five widely used generative models and reveal four typical failure modes: (1) We find a variety of natural text prompts that generate images failing to capture the semantics of input texts. We further discuss the underlying causes and potential solutions based on the results. (2) We find regions in the latent space that lead to distorted images independent of the text prompt, suggesting that parts of the latent space are not well-structured. (3) We also find latent samples that result in natural-looking images unrelated to the text prompt, implying a possible misalignment between the latent and prompt spaces. (4) By appending a single adversarial token embedding to any input prompts, we can generate a variety of specified target objects. Project page: https://sage-diffusion.github.io/

Latent diffusion models (LDMs) have made significant advancements in the field of image generation in recent years. One major advantage of LDMs is their ability to operate in a compressed latent space, allowing for more efficient training and deployment. However, despite these advantages, challenges with LDMs still remain. For example, it has been observed that LDMs often generate high-frequency details and complex compositions imperfectly. We hypothesize that one reason for these flaws is due to the fact that all pre- and post-training of LDMs are done in latent space, which is typically 8 times 8 lower spatial-resolution than the output images. To address this issue, we propose adding pixel-space supervision in the post-training process to better preserve high-frequency details. Experimentally, we show that adding a pixel-space objective significantly improves both supervised quality fine-tuning and preference-based post-training by a large margin on a state-of-the-art DiT transformer and U-Net diffusion models in both visual quality and visual flaw metrics, while maintaining the same text alignment quality.

Instead of performing text-conditioned denoising in the image domain, latent diffusion models (LDMs) operate in latent space of a variational autoencoder (VAE), enabling more efficient processing at reduced computational costs. However, while the diffusion process has moved to the latent space, the contrastive language-image pre-training (CLIP) models, as used in many image processing tasks, still operate in pixel space. Doing so requires costly VAE-decoding of latent images before they can be processed. In this paper, we introduce Latent-CLIP, a CLIP model that operates directly in the latent space. We train Latent-CLIP on 2.7B pairs of latent images and descriptive texts, and show that it matches zero-shot classification performance of similarly sized CLIP models on both the ImageNet benchmark and a LDM-generated version of it, demonstrating its effectiveness in assessing both real and generated content. Furthermore, we construct Latent-CLIP rewards for reward-based noise optimization (ReNO) and show that they match the performance of their CLIP counterparts on GenEval and T2I-CompBench while cutting the cost of the total pipeline by 21%. Finally, we use Latent-CLIP to guide generation away from harmful content, achieving strong performance on the inappropriate image prompts (I2P) benchmark and a custom evaluation, without ever requiring the costly step of decoding intermediate images.

Powerful generative models, particularly in Natural Language Modelling, are commonly trained by maximizing a variational lower bound on the data log likelihood. These models often suffer from poor use of their latent variable, with ad-hoc annealing factors used to encourage retention of information in the latent variable. We discuss an alternative and general approach to latent variable modelling, based on an objective that combines the data log likelihood as well as the likelihood of a perfect reconstruction through an autoencoder. Tying these together ensures by design that the latent variable captures information about the observations, whilst retaining the ability to generate well. Interestingly, though this approach is a priori unrelated to VAEs, the lower bound attained is identical to the standard VAE bound but with the addition of a simple pre-factor; thus, providing a formal interpretation of the commonly used, ad-hoc pre-factors in training VAEs.

In image generation, Multiple Latent Variable Generative Models (MLVGMs) employ multiple latent variables to gradually shape the final images, from global characteristics to finer and local details (e.g., StyleGAN, NVAE), emerging as powerful tools for diverse applications. Yet their generative dynamics remain only empirically observed, without a systematic understanding of each latent variable's impact. In this work, we propose a novel framework that quantifies the contribution of each latent variable using Mutual Information (MI) as a metric. Our analysis reveals that current MLVGMs often underutilize some latent variables, and provides actionable insights for their use in downstream applications. With this foundation, we introduce a method for generating synthetic data for Self-Supervised Contrastive Representation Learning (SSCRL). By leveraging the hierarchical and disentangled variables of MLVGMs, our approach produces diverse and semantically meaningful views without the need for real image data. Additionally, we introduce a Continuous Sampling (CS) strategy, where the generator dynamically creates new samples during SSCRL training, greatly increasing data variability. Our comprehensive experiments demonstrate the effectiveness of these contributions, showing that MLVGMs' generated views compete on par with or even surpass views generated from real data. This work establishes a principled approach to understanding and exploiting MLVGMs, advancing both generative modeling and self-supervised learning. Code and pre-trained models at: https://github.com/SerezD/mi_ml_gen.

Variational autoencoders (VAEs) are one of the powerful unsupervised learning frameworks in NLP for latent representation learning and latent-directed generation. The classic optimization goal of VAEs is to maximize the Evidence Lower Bound (ELBo), which consists of a conditional likelihood for generation and a negative Kullback-Leibler (KL) divergence for regularization. In practice, optimizing ELBo often leads the posterior distribution of all samples converge to the same degenerated local optimum, namely posterior collapse or KL vanishing. There are effective ways proposed to prevent posterior collapse in VAEs, but we observe that they in essence make trade-offs between posterior collapse and hole problem, i.e., mismatch between the aggregated posterior distribution and the prior distribution. To this end, we introduce new training objectives to tackle both two problems through a novel regularization based on the probabilistic density gap between the aggregated posterior distribution and the prior distribution. Through experiments on language modeling, latent space visualization and interpolation, we show that our proposed method can solve both problems effectively and thus outperforms the existing methods in latent-directed generation. To the best of our knowledge, we are the first to jointly solve the hole problem and the posterior collapse.

Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related) domains, we expand the generator to jointly model all domains, old and new, harmoniously. First, we note the generator contains a meaningful, pretrained latent space. Is it possible to minimally perturb this hard-earned representation, while maximally representing the new domains? Interestingly, we find that the latent space offers unused, "dormant" directions, which do not affect the output. This provides an opportunity: By "repurposing" these directions, we can represent new domains without perturbing the original representation. In fact, we find that pretrained generators have the capacity to add several - even hundreds - of new domains! Using our expansion method, one "expanded" model can supersede numerous domain-specific models, without expanding the model size. Additionally, a single expanded generator natively supports smooth transitions between domains, as well as composition of domains. Code and project page available at https://yotamnitzan.github.io/domain-expansion/.

Diffusion probabilistic models have been shown to generate state-of-the-art results on several competitive image synthesis benchmarks but lack a low-dimensional, interpretable latent space, and are slow at generation. On the other hand, standard Variational Autoencoders (VAEs) typically have access to a low-dimensional latent space but exhibit poor sample quality. We present DiffuseVAE, a novel generative framework that integrates VAE within a diffusion model framework, and leverage this to design novel conditional parameterizations for diffusion models. We show that the resulting model equips diffusion models with a low-dimensional VAE inferred latent code which can be used for downstream tasks like controllable synthesis. The proposed method also improves upon the speed vs quality tradeoff exhibited in standard unconditional DDPM/DDIM models (for instance, FID of 16.47 vs 34.36 using a standard DDIM on the CelebA-HQ-128 benchmark using T=10 reverse process steps) without having explicitly trained for such an objective. Furthermore, the proposed model exhibits synthesis quality comparable to state-of-the-art models on standard image synthesis benchmarks like CIFAR-10 and CelebA-64 while outperforming most existing VAE-based methods. Lastly, we show that the proposed method exhibits inherent generalization to different types of noise in the conditioning signal. For reproducibility, our source code is publicly available at https://github.com/kpandey008/DiffuseVAE.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete mixtures represented as computational graphs composed of input, sum and product units. Unlike continuous LV models, PCs provide tractable inference but are limited to discrete LVs with categorical (i.e. unordered) states. We bridge these model classes by introducing probabilistic integral circuits (PICs), a new language of computational graphs that extends PCs with integral units representing continuous LVs. In the first place, PICs are symbolic computational graphs and are fully tractable in simple cases where analytical integration is possible. In practice, we parameterise PICs with light-weight neural nets delivering an intractable hierarchical continuous mixture that can be approximated arbitrarily well with large PCs using numerical quadrature. On several distribution estimation benchmarks, we show that such PIC-approximating PCs systematically outperform PCs commonly learned via expectation-maximization or SGD.

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `h-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The h-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.

This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the underlying distribution. This fixed flow model subsequently regularizes the latent space via an alignment loss, which reformulates the flow matching objective to treat the latents as optimization targets. We formally prove that minimizing this alignment loss establishes a computationally tractable surrogate objective for maximizing a variational lower bound on the log-likelihood of latents under the target distribution. Notably, the proposed method eliminates computationally expensive likelihood evaluations and avoids ODE solving during optimization. As a proof of concept, we demonstrate in a controlled setting that the alignment loss landscape closely approximates the negative log-likelihood of the target distribution. We further validate the effectiveness of our approach through large-scale image generation experiments on ImageNet with diverse target distributions, accompanied by detailed discussions and ablation studies. With both theoretical and empirical validation, our framework paves a new way for latent space alignment.

Latent generative modeling, where a pretrained autoencoder maps pixels into a latent space for the diffusion process, has become the standard strategy for Diffusion Transformers (DiT); however, the autoencoder component has barely evolved. Most DiTs continue to rely on the original VAE encoder, which introduces several limitations: outdated backbones that compromise architectural simplicity, low-dimensional latent spaces that restrict information capacity, and weak representations that result from purely reconstruction-based training and ultimately limit generative quality. In this work, we explore replacing the VAE with pretrained representation encoders (e.g., DINO, SigLIP, MAE) paired with trained decoders, forming what we term Representation Autoencoders (RAEs). These models provide both high-quality reconstructions and semantically rich latent spaces, while allowing for a scalable transformer-based architecture. Since these latent spaces are typically high-dimensional, a key challenge is enabling diffusion transformers to operate effectively within them. We analyze the sources of this difficulty, propose theoretically motivated solutions, and validate them empirically. Our approach achieves faster convergence without auxiliary representation alignment losses. Using a DiT variant equipped with a lightweight, wide DDT head, we achieve strong image generation results on ImageNet: 1.51 FID at 256x256 (no guidance) and 1.13 at both 256x256 and 512x512 (with guidance). RAE offers clear advantages and should be the new default for diffusion transformer training.

Many approaches in generalized zero-shot learning rely on cross-modal mapping between the image feature space and the class embedding space. As labeled images are expensive, one direction is to augment the dataset by generating either images or image features. However, the former misses fine-grained details and the latter requires learning a mapping associated with class embeddings. In this work, we take feature generation one step further and propose a model where a shared latent space of image features and class embeddings is learned by modality-specific aligned variational autoencoders. This leaves us with the required discriminative information about the image and classes in the latent features, on which we train a softmax classifier. The key to our approach is that we align the distributions learned from images and from side-information to construct latent features that contain the essential multi-modal information associated with unseen classes. We evaluate our learned latent features on several benchmark datasets, i.e. CUB, SUN, AWA1 and AWA2, and establish a new state of the art on generalized zero-shot as well as on few-shot learning. Moreover, our results on ImageNet with various zero-shot splits show that our latent features generalize well in large-scale settings.

The steep computational cost of diffusion models at inference hinders their use as fast physics emulators. In the context of image and video generation, this computational drawback has been addressed by generating in the latent space of an autoencoder instead of the pixel space. In this work, we investigate whether a similar strategy can be effectively applied to the emulation of dynamical systems and at what cost. We find that the accuracy of latent-space emulation is surprisingly robust to a wide range of compression rates (up to 1000x). We also show that diffusion-based emulators are consistently more accurate than non-generative counterparts and compensate for uncertainty in their predictions with greater diversity. Finally, we cover practical design choices, spanning from architectures to optimizers, that we found critical to train latent-space emulators.

Generative autoencoders offer a promising approach for controllable text generation by leveraging their latent sentence representations. However, current models struggle to maintain coherent latent spaces required to perform meaningful text manipulations via latent vector operations. Specifically, we demonstrate by example that neural encoders do not necessarily map similar sentences to nearby latent vectors. A theoretical explanation for this phenomenon establishes that high capacity autoencoders can learn an arbitrary mapping between sequences and associated latent representations. To remedy this issue, we augment adversarial autoencoders with a denoising objective where original sentences are reconstructed from perturbed versions (referred to as DAAE). We prove that this simple modification guides the latent space geometry of the resulting model by encouraging the encoder to map similar texts to similar latent representations. In empirical comparisons with various types of autoencoders, our model provides the best trade-off between generation quality and reconstruction capacity. Moreover, the improved geometry of the DAAE latent space enables zero-shot text style transfer via simple latent vector arithmetic.

Generative models have been very popular in the recent years for their image generation capabilities. GAN-based models are highly regarded for their disentangled latent space, which is a key feature contributing to their success in controlled image editing. On the other hand, diffusion models have emerged as powerful tools for generating high-quality images. However, the latent space of diffusion models is not as thoroughly explored or understood. Existing methods that aim to explore the latent space of diffusion models usually relies on text prompts to pinpoint specific semantics. However, this approach may be restrictive in areas such as art, fashion, or specialized fields like medicine, where suitable text prompts might not be available or easy to conceive thus limiting the scope of existing work. In this paper, we propose an unsupervised method to discover latent semantics in text-to-image diffusion models without relying on text prompts. Our method takes a small set of unlabeled images from specific domains, such as faces or cats, and a pre-trained diffusion model, and discovers diverse semantics in unsupervised fashion using a contrastive learning objective. Moreover, the learned directions can be applied simultaneously, either within the same domain (such as various types of facial edits) or across different domains (such as applying cat and face edits within the same image) without interfering with each other. Our extensive experiments show that our method achieves highly disentangled edits, outperforming existing approaches in both diffusion-based and GAN-based latent space editing methods.

Fine-tuning large language models (LLMs) for recommendation in a generative manner has delivered promising results, but encounters significant inference overhead due to autoregressive decoding in the language space. This work explores bypassing language-space decoding by directly matching candidate items with the LLM's internal thought representations in the latent space, eliminating the time-consuming autoregressive process to reduce computational costs. Towards this, we introduce Light Latent-space Decoding (L2D), an effective and efficient latent-space decoding method. L2D represents user-preferred items by using the hidden states of test sequences reflecting the LLM's internal thought, and obtains candidate item representations from the hidden states of training sequences labeled with the corresponding candidate items. It then matches the two types of representations to decode items, achieving latent-space decoding. In this way, it enables efficient decoding without altering the LLM's generative tuning paradigm, thereby preserving performance. Extensive empirical results demonstrate that L2D is more than 10x faster than language-space decoding while maintaining or enhancing performance.

3D molecule generation is crucial for drug discovery and material science, requiring models to process complex multi-modalities, including atom types, chemical bonds, and 3D coordinates. A key challenge is integrating these modalities of different shapes while maintaining SE(3) equivariance for 3D coordinates. To achieve this, existing approaches typically maintain separate latent spaces for invariant and equivariant modalities, reducing efficiency in both training and sampling. In this work, we propose Unified Variational Auto-Encoder for 3D Molecular Latent Diffusion Modeling (UAE-3D), a multi-modal VAE that compresses 3D molecules into latent sequences from a unified latent space, while maintaining near-zero reconstruction error. This unified latent space eliminates the complexities of handling multi-modality and equivariance when performing latent diffusion modeling. We demonstrate this by employing the Diffusion Transformer--a general-purpose diffusion model without any molecular inductive bias--for latent generation. Extensive experiments on GEOM-Drugs and QM9 datasets demonstrate that our method significantly establishes new benchmarks in both de novo and conditional 3D molecule generation, achieving leading efficiency and quality.

Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward chi^2 divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.

We learn a latent space for easy capture, consistent interpolation, and efficient reproduction of visual material appearance. When users provide a photo of a stationary natural material captured under flashlight illumination, first it is converted into a latent material code. Then, in the second step, conditioned on the material code, our method produces an infinite and diverse spatial field of BRDF model parameters (diffuse albedo, normals, roughness, specular albedo) that subsequently allows rendering in complex scenes and illuminations, matching the appearance of the input photograph. Technically, we jointly embed all flash images into a latent space using a convolutional encoder, and -- conditioned on these latent codes -- convert random spatial fields into fields of BRDF parameters using a convolutional neural network (CNN). We condition these BRDF parameters to match the visual characteristics (statistics and spectra of visual features) of the input under matching light. A user study compares our approach favorably to previous work, even those with access to BRDF supervision.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

Recent state-of-the-art authorship attribution methods learn authorship representations of texts in a latent, non-interpretable space, hindering their usability in real-world applications. Our work proposes a novel approach to interpreting these learned embeddings by identifying representative points in the latent space and utilizing LLMs to generate informative natural language descriptions of the writing style of each point. We evaluate the alignment of our interpretable space with the latent one and find that it achieves the best prediction agreement compared to other baselines. Additionally, we conduct a human evaluation to assess the quality of these style descriptions, validating their utility as explanations for the latent space. Finally, we investigate whether human performance on the challenging AA task improves when aided by our system's explanations, finding an average improvement of around +20% in accuracy.

Visual generative models (e.g., diffusion models) typically operate in compressed latent spaces to balance training efficiency and sample quality. In parallel, there has been growing interest in leveraging high-quality pre-trained visual representations, either by aligning them inside VAEs or directly within the generative model. However, adapting such representations remains challenging due to fundamental mismatches between understanding-oriented features and generation-friendly latent spaces. Representation encoders benefit from high-dimensional latents that capture diverse hypotheses for masked regions, whereas generative models favor low-dimensional latents that must faithfully preserve injected noise. This discrepancy has led prior work to rely on complex objectives and architectures. In this work, we propose FAE (Feature Auto-Encoder), a simple yet effective framework that adapts pre-trained visual representations into low-dimensional latents suitable for generation using as little as a single attention layer, while retaining sufficient information for both reconstruction and understanding. The key is to couple two separate deep decoders: one trained to reconstruct the original feature space, and a second that takes the reconstructed features as input for image generation. FAE is generic; it can be instantiated with a variety of self-supervised encoders (e.g., DINO, SigLIP) and plugged into two distinct generative families: diffusion models and normalizing flows. Across class-conditional and text-to-image benchmarks, FAE achieves strong performance. For example, on ImageNet 256x256, our diffusion model with CFG attains a near state-of-the-art FID of 1.29 (800 epochs) and 1.70 (80 epochs). Without CFG, FAE reaches the state-of-the-art FID of 1.48 (800 epochs) and 2.08 (80 epochs), demonstrating both high quality and fast learning.

Temporal abstraction and efficient planning pose significant challenges in offline reinforcement learning, mainly when dealing with domains that involve temporally extended tasks and delayed sparse rewards. Existing methods typically plan in the raw action space and can be inefficient and inflexible. Latent action spaces offer a more flexible paradigm, capturing only possible actions within the behavior policy support and decoupling the temporal structure between planning and modeling. However, current latent-action-based methods are limited to discrete spaces and require expensive planning. This paper presents a unified framework for continuous latent action space representation learning and planning by leveraging latent, score-based diffusion models. We establish the theoretical equivalence between planning in the latent action space and energy-guided sampling with a pretrained diffusion model and incorporate a novel sequence-level exact sampling method. Our proposed method, LatentDiffuser, demonstrates competitive performance on low-dimensional locomotion control tasks and surpasses existing methods in higher-dimensional tasks.

Different from human nature, it is still common practice today for vision tasks to train deep learning models only initially and on fixed datasets. A variety of approaches have recently addressed handling continual data streams. However, extending these methods to manage out-of-distribution (OOD) scenarios has not effectively been investigated. On the other hand, it has recently been shown that non-continual neural mesh models exhibit strong performance in generalizing to such OOD scenarios. To leverage this decisive property in a continual learning setting, we propose incremental neural mesh models that can be extended with new meshes over time. In addition, we present a latent space initialization strategy that enables us to allocate feature space for future unseen classes in advance and a positional regularization term that forces the features of the different classes to consistently stay in respective latent space regions. We demonstrate the effectiveness of our method through extensive experiments on the Pascal3D and ObjectNet3D datasets and show that our approach outperforms the baselines for classification by 2-6% in the in-domain and by 6-50% in the OOD setting. Our work also presents the first incremental learning approach for pose estimation. Our code and model can be found at https://github.com/Fischer-Tom/iNeMo.

Deep generative models are routinely used in generating samples from complex, high-dimensional distributions. Despite their apparent successes, their statistical properties are not well understood. A common assumption is that with enough training data and sufficiently large neural networks, deep generative model samples will have arbitrarily small errors in sampling from any continuous target distribution. We set up a unifying framework that debunks this belief. We demonstrate that broad classes of deep generative models, including variational autoencoders and generative adversarial networks, are not universal generators. Under the predominant case of Gaussian latent variables, these models can only generate concentrated samples that exhibit light tails. Using tools from concentration of measure and convex geometry, we give analogous results for more general log-concave and strongly log-concave latent variable distributions. We extend our results to diffusion models via a reduction argument. We use the Gromov--Levy inequality to give similar guarantees when the latent variables lie on manifolds with positive Ricci curvature. These results shed light on the limited capacity of common deep generative models to handle heavy tails. We illustrate the empirical relevance of our work with simulations and financial data.

Multimodal generative models require a unified approach to handle both discrete data (e.g., text and code) and continuous data (e.g., image, audio, video). In this work, we propose Latent Language Modeling (LatentLM), which seamlessly integrates continuous and discrete data using causal Transformers. Specifically, we employ a variational autoencoder (VAE) to represent continuous data as latent vectors and introduce next-token diffusion for autoregressive generation of these vectors. Additionally, we develop sigma-VAE to address the challenges of variance collapse, which is crucial for autoregressive modeling. Extensive experiments demonstrate the effectiveness of LatentLM across various modalities. In image generation, LatentLM surpasses Diffusion Transformers in both performance and scalability. When integrated into multimodal large language models, LatentLM provides a general-purpose interface that unifies multimodal generation and understanding. Experimental results show that LatentLM achieves favorable performance compared to Transfusion and vector quantized models in the setting of scaling up training tokens. In text-to-speech synthesis, LatentLM outperforms the state-of-the-art VALL-E 2 model in speaker similarity and robustness, while requiring 10x fewer decoding steps. The results establish LatentLM as a highly effective and scalable approach to advance large multimodal models.

Most visual generative models compress images into a latent space before applying diffusion or autoregressive modelling. Yet, existing approaches such as VAEs and foundation model aligned encoders implicitly constrain the latent space without explicitly shaping its distribution, making it unclear which types of distributions are optimal for modeling. We introduce Distribution-Matching VAE (DMVAE), which explicitly aligns the encoder's latent distribution with an arbitrary reference distribution via a distribution matching constraint. This generalizes beyond the Gaussian prior of conventional VAEs, enabling alignment with distributions derived from self-supervised features, diffusion noise, or other prior distributions. With DMVAE, we can systematically investigate which latent distributions are more conducive to modeling, and we find that SSL-derived distributions provide an excellent balance between reconstruction fidelity and modeling efficiency, reaching gFID equals 3.2 on ImageNet with only 64 training epochs. Our results suggest that choosing a suitable latent distribution structure (achieved via distribution-level alignment), rather than relying on fixed priors, is key to bridging the gap between easy-to-model latents and high-fidelity image synthesis. Code is avaliable at https://github.com/sen-ye/dmvae.

Generative Adversarial Networks (GANs) have been widely applied in modeling diverse image distributions. However, despite its impressive applications, the structure of the latent space in GANs largely remains as a black-box, leaving its controllable generation an open problem, especially when spurious correlations between different semantic attributes exist in the image distributions. To address this problem, previous methods typically learn linear directions or individual channels that control semantic attributes in the image space. However, they often suffer from imperfect disentanglement, or are unable to obtain multi-directional controls. In this work, in light of the above challenges, we propose a novel approach that discovers nonlinear controls, which enables multi-directional manipulation as well as effective disentanglement, based on gradient information in the learned GAN latent space. More specifically, we first learn interpolation directions by following the gradients from classification networks trained separately on the attributes, and then navigate the latent space by exclusively controlling channels activated for the target attribute in the learned directions. Empirically, with small training data, our approach is able to gain fine-grained controls over a diverse set of bi-directional and multi-directional attributes, and we showcase its ability to achieve disentanglement significantly better than state-of-the-art methods both qualitatively and quantitatively.

In recent years supervised representation learning has provided state of the art or close to the state of the art results in semantic analysis tasks including ranking and information retrieval. The core idea is to learn how to embed items into a latent space such that they optimize a supervised objective in that latent space. The dimensions of the latent space have no clear semantics, and this reduces the interpretability of the system. For example, in personalization models, it is hard to explain why a particular item is ranked high for a given user profile. We propose a novel model of representation learning called Supervised Explicit Semantic Analysis (SESA) that is trained in a supervised fashion to embed items to a set of dimensions with explicit semantics. The model learns to compare two objects by representing them in this explicit space, where each dimension corresponds to a concept from a knowledge base. This work extends Explicit Semantic Analysis (ESA) with a supervised model for ranking problems. We apply this model to the task of Job-Profile relevance in LinkedIn in which a set of skills defines our explicit dimensions of the space. Every profile and job are encoded to this set of skills their similarity is calculated in this space. We use RNNs to embed text input into this space. In addition to interpretability, our model makes use of the web-scale collaborative skills data that is provided by users for each LinkedIn profile. Our model provides state of the art result while it remains interpretable.

Document editing has become a pervasive component of the production of information, with version control systems enabling edits to be efficiently stored and applied. In light of this, the task of learning distributed representations of edits has been recently proposed. With this in mind, we propose a novel approach that employs variational inference to learn a continuous latent space of vector representations to capture the underlying semantic information with regard to the document editing process. We achieve this by introducing a latent variable to explicitly model the aforementioned features. This latent variable is then combined with a document representation to guide the generation of an edited version of this document. Additionally, to facilitate standardized automatic evaluation of edit representations, which has heavily relied on direct human input thus far, we also propose a suite of downstream tasks, PEER, specifically designed to measure the quality of edit representations in the context of natural language processing.

Jointly identifying a mixture of discrete and continuous factors of variability without supervision is a key problem in unraveling complex phenomena. Variational inference has emerged as a promising method to learn interpretable mixture representations. However, posterior approximation in high-dimensional latent spaces, particularly for discrete factors remains challenging. Here, we propose an unsupervised variational framework using multiple interacting networks called cpl-mixVAE that scales well to high-dimensional discrete settings. In this framework, the mixture representation of each network is regularized by imposing a consensus constraint on the discrete factor. We justify the use of this framework by providing both theoretical and experimental results. Finally, we use the proposed method to jointly uncover discrete and continuous factors of variability describing gene expression in a single-cell transcriptomic dataset profiling more than a hundred cortical neuron types.

With generative models producing high quality images that are indistinguishable from real ones, there is growing concern regarding the malicious usage of AI-generated images. Imperceptible image watermarking is one viable solution towards such concerns. Prior watermarking methods map the image to a latent space for adding the watermark. Moreover, Latent Diffusion Models (LDM) generate the image in the latent space of a pre-trained autoencoder. We argue that this latent space can be used to integrate watermarking into the generation process. To this end, we present LaWa, an in-generation image watermarking method designed for LDMs. By using coarse-to-fine watermark embedding modules, LaWa modifies the latent space of pre-trained autoencoders and achieves high robustness against a wide range of image transformations while preserving perceptual quality of the image. We show that LaWa can also be used as a general image watermarking method. Through extensive experiments, we demonstrate that LaWa outperforms previous works in perceptual quality, robustness against attacks, and computational complexity, while having very low false positive rate. Code is available here.

Latent space exploration is a technique that discovers interpretable latent directions and manipulates latent codes to edit various attributes in images generated by generative adversarial networks (GANs). However, in previous work, spatial control is limited to simple transformations (e.g., translation and rotation), and it is laborious to identify appropriate latent directions and adjust their parameters. In this paper, we tackle the problem of editing the StyleGAN image layout by annotating the image directly. To do so, we propose an interactive framework for manipulating latent codes in accordance with the user inputs. In our framework, the user annotates a StyleGAN image with locations they want to move or not and specifies a movement direction by mouse dragging. From these user inputs and initial latent codes, our latent transformer based on a transformer encoder-decoder architecture estimates the output latent codes, which are fed to the StyleGAN generator to obtain a result image. To train our latent transformer, we utilize synthetic data and pseudo-user inputs generated by off-the-shelf StyleGAN and optical flow models, without manual supervision. Quantitative and qualitative evaluations demonstrate the effectiveness of our method over existing methods.

Causal representation learning has showed a variety of settings in which we can disentangle latent variables with identifiability guarantees (up to some reasonable equivalence class). Common to all of these approaches is the assumption that (1) the latent variables are represented as d-dimensional vectors, and (2) that the observations are the output of some injective generative function of these latent variables. While these assumptions appear benign, we show that when the observations are of multiple objects, the generative function is no longer injective and disentanglement fails in practice. We can address this failure by combining recent developments in object-centric learning and causal representation learning. By modifying the Slot Attention architecture arXiv:2006.15055, we develop an object-centric architecture that leverages weak supervision from sparse perturbations to disentangle each object's properties. This approach is more data-efficient in the sense that it requires significantly fewer perturbations than a comparable approach that encodes to a Euclidean space and we show that this approach successfully disentangles the properties of a set of objects in a series of simple image-based disentanglement experiments.

AI-generated content has attracted lots of attention recently, but photo-realistic video synthesis is still challenging. Although many attempts using GANs and autoregressive models have been made in this area, the visual quality and length of generated videos are far from satisfactory. Diffusion models have shown remarkable results recently but require significant computational resources. To address this, we introduce lightweight video diffusion models by leveraging a low-dimensional 3D latent space, significantly outperforming previous pixel-space video diffusion models under a limited computational budget. In addition, we propose hierarchical diffusion in the latent space such that longer videos with more than one thousand frames can be produced. To further overcome the performance degradation issue for long video generation, we propose conditional latent perturbation and unconditional guidance that effectively mitigate the accumulated errors during the extension of video length. Extensive experiments on small domain datasets of different categories suggest that our framework generates more realistic and longer videos than previous strong baselines. We additionally provide an extension to large-scale text-to-video generation to demonstrate the superiority of our work. Our code and models will be made publicly available.

We investigate feature universality in large language models (LLMs), a research field that aims to understand how different models similarly represent concepts in the latent spaces of their intermediate layers. Demonstrating feature universality allows discoveries about latent representations to generalize across several models. However, comparing features across LLMs is challenging due to polysemanticity, in which individual neurons often correspond to multiple features rather than distinct ones. This makes it difficult to disentangle and match features across different models. To address this issue, we employ a method known as dictionary learning by using sparse autoencoders (SAEs) to transform LLM activations into more interpretable spaces spanned by neurons corresponding to individual features. After matching feature neurons across models via activation correlation, we apply representational space similarity metrics like Singular Value Canonical Correlation Analysis to analyze these SAE features across different LLMs. Our experiments reveal significant similarities in SAE feature spaces across various LLMs, providing new evidence for feature universality.

The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently proposed generative model pairing a top-down generative network with a bottom-up recognition network which approximates posterior inference. It typically makes strong assumptions about posterior inference, for instance that the posterior distribution is approximately factorial, and that its parameters can be approximated with nonlinear regression from the observations. As we show empirically, the VAE objective can lead to overly simplified representations which fail to use the network's entire modeling capacity. We present the importance weighted autoencoder (IWAE), a generative model with the same architecture as the VAE, but which uses a strictly tighter log-likelihood lower bound derived from importance weighting. In the IWAE, the recognition network uses multiple samples to approximate the posterior, giving it increased flexibility to model complex posteriors which do not fit the VAE modeling assumptions. We show empirically that IWAEs learn richer latent space representations than VAEs, leading to improved test log-likelihood on density estimation benchmarks.

While diffusion models excel at generating high-quality images from text prompts, they struggle with visual consistency in image sequences. Existing methods generate each image independently, leading to disjointed narratives - a challenge further exacerbated in non-linear storytelling, where scenes must connect beyond adjacent frames. We introduce a novel beam search strategy for latent space exploration, enabling conditional generation of full image sequences with beam search decoding. Unlike prior approaches that use fixed latent priors, our method dynamically searches for an optimal sequence of latent representations, ensuring coherent visual transitions. To address beam search's quadratic complexity, we integrate a cross-attention mechanism that efficiently scores search paths and enables pruning, prioritizing alignment with both textual prompts and visual context. Human evaluations confirm that our approach outperforms baseline methods, producing full sequences with superior coherence, visual continuity, and textual alignment. By bridging advances in search optimization and latent space refinement, this work sets a new standard for structured image sequence generation.

Recently, parallel text generation has received widespread attention due to its success in generation efficiency. Although many advanced techniques are proposed to improve its generation quality, they still need the help of an autoregressive model for training to overcome the one-to-many multi-modal phenomenon in the dataset, limiting their applications. In this paper, we propose latent-GLAT, which employs the discrete latent variables to capture word categorical information and invoke an advanced curriculum learning technique, alleviating the multi-modality problem. Experiment results show that our method outperforms strong baselines without the help of an autoregressive model, which further broadens the application scenarios of the parallel decoding paradigm.

Recent progress in diffusion-based visual generation has largely relied on latent diffusion models with variational autoencoders (VAEs). While effective for high-fidelity synthesis, this VAE+diffusion paradigm suffers from limited training efficiency, slow inference, and poor transferability to broader vision tasks. These issues stem from a key limitation of VAE latent spaces: the lack of clear semantic separation and strong discriminative structure. Our analysis confirms that these properties are crucial not only for perception and understanding tasks, but also for the stable and efficient training of latent diffusion models. Motivated by this insight, we introduce SVG, a novel latent diffusion model without variational autoencoders, which leverages self-supervised representations for visual generation. SVG constructs a feature space with clear semantic discriminability by leveraging frozen DINO features, while a lightweight residual branch captures fine-grained details for high-fidelity reconstruction. Diffusion models are trained directly on this semantically structured latent space to facilitate more efficient learning. As a result, SVG enables accelerated diffusion training, supports few-step sampling, and improves generative quality. Experimental results further show that SVG preserves the semantic and discriminative capabilities of the underlying self-supervised representations, providing a principled pathway toward task-general, high-quality visual representations.

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

While 3D content generation has advanced significantly, existing methods still face challenges with input formats, latent space design, and output representations. This paper introduces a novel 3D generation framework that addresses these challenges, offering scalable, high-quality 3D generation with an interactive Point Cloud-structured Latent space. Our framework employs a Variational Autoencoder (VAE) with multi-view posed RGB-D(epth)-N(ormal) renderings as input, using a unique latent space design that preserves 3D shape information, and incorporates a cascaded latent diffusion model for improved shape-texture disentanglement. The proposed method, GaussianAnything, supports multi-modal conditional 3D generation, allowing for point cloud, caption, and single/multi-view image inputs. Notably, the newly proposed latent space naturally enables geometry-texture disentanglement, thus allowing 3D-aware editing. Experimental results demonstrate the effectiveness of our approach on multiple datasets, outperforming existing methods in both text- and image-conditioned 3D generation.

In disentangled representation learning, a model is asked to tease apart a dataset's underlying sources of variation and represent them independently of one another. Since the model is provided with no ground truth information about these sources, inductive biases take a paramount role in enabling disentanglement. In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. Concretely, we do this by (i) quantizing the latent space into discrete code vectors with a separate learnable scalar codebook per dimension and (ii) applying strong model regularization via an unusually high weight decay. Intuitively, the latent space design forces the encoder to combinatorially construct codes from a small number of distinct scalar values, which in turn enables the decoder to assign a consistent meaning to each value. Regularization then serves to drive the model towards this parsimonious strategy. We demonstrate the broad applicability of this approach by adding it to both basic data-reconstructing (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models. For reliable evaluation, we also propose InfoMEC, a new set of metrics for disentanglement that is cohesively grounded in information theory and fixes well-established shortcomings in previous metrics. Together with regularization, latent quantization dramatically improves the modularity and explicitness of learned representations on a representative suite of benchmark datasets. In particular, our quantized-latent autoencoder (QLAE) consistently outperforms strong methods from prior work in these key disentanglement properties without compromising data reconstruction.

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a lower-dimensional space, which is crucial for effective data representation. To address this limitation, we propose a novel approach called Low-Rank Autoencoder (LoRAE). In LoRAE, we incorporated a low-rank regularizer to adaptively reconstruct a low-dimensional latent space while preserving the basic objective of an autoencoder. This helps embed the data in a lower-dimensional space while preserving important information. It is a simple autoencoder extension that learns low-rank latent space. Theoretically, we establish a tighter error bound for our model. Empirically, our model's superiority shines through various tasks such as image generation and downstream classification. Both theoretical and practical outcomes highlight the importance of acquiring low-dimensional embeddings.

Despite their tremendous success in modelling high-dimensional data manifolds, deep neural networks suffer from the threat of adversarial attacks - Existence of perceptually valid input-like samples obtained through careful perturbation that lead to degradation in the performance of the underlying model. Major concerns with existing defense mechanisms include non-generalizability across different attacks, models and large inference time. In this paper, we propose a generalized defense mechanism capitalizing on the expressive power of regularized latent space based generative models. We design an adversarial filter, devoid of access to classifier and adversaries, which makes it usable in tandem with any classifier. The basic idea is to learn a Lipschitz constrained mapping from the data manifold, incorporating adversarial perturbations, to a quantized latent space and re-map it to the true data manifold. Specifically, we simultaneously auto-encode the data manifold and its perturbations implicitly through the perturbations of the regularized and quantized generative latent space, realized using variational inference. We demonstrate the efficacy of the proposed formulation in providing resilience against multiple attack types (black and white box) and methods, while being almost real-time. Our experiments show that the proposed method surpasses the state-of-the-art techniques in several cases.

In this paper, we learn disentangled representations of timbre and pitch for musical instrument sounds. We adapt a framework based on variational autoencoders with Gaussian mixture latent distributions. Specifically, we use two separate encoders to learn distinct latent spaces for timbre and pitch, which form Gaussian mixture components representing instrument identity and pitch, respectively. For reconstruction, latent variables of timbre and pitch are sampled from corresponding mixture components, and are concatenated as the input to a decoder. We show the model efficacy by latent space visualization, and a quantitative analysis indicates the discriminability of these spaces, even with a limited number of instrument labels for training. The model allows for controllable synthesis of selected instrument sounds by sampling from the latent spaces. To evaluate this, we trained instrument and pitch classifiers using original labeled data. These classifiers achieve high accuracy when tested on our synthesized sounds, which verifies the model performance of controllable realistic timbre and pitch synthesis. Our model also enables timbre transfer between multiple instruments, with a single autoencoder architecture, which is evaluated by measuring the shift in posterior of instrument classification. Our in depth evaluation confirms the model ability to successfully disentangle timbre and pitch.

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.

We investigate the construction of latent spaces through self-supervised learning to support semantically meaningful operations. Analogous to operational amplifiers, these "operational latent spaces" (OpLaS) not only demonstrate semantic structure such as clustering but also support common transformational operations with inherent semantic meaning. Some operational latent spaces are found to have arisen "unintentionally" in the progress toward some (other) self-supervised learning objective, in which unintended but still useful properties are discovered among the relationships of points in the space. Other spaces may be constructed "intentionally" by developers stipulating certain kinds of clustering or transformations intended to produce the desired structure. We focus on the intentional creation of operational latent spaces via self-supervised learning, including the introduction of rotation operators via a novel "FiLMR" layer, which can be used to enable ring-like symmetries found in some musical constructions.

Offline reinforcement learning (RL) holds promise as a means to learn high-reward policies from a static dataset, without the need for further environment interactions. However, a key challenge in offline RL lies in effectively stitching portions of suboptimal trajectories from the static dataset while avoiding extrapolation errors arising due to a lack of support in the dataset. Existing approaches use conservative methods that are tricky to tune and struggle with multi-modal data (as we show) or rely on noisy Monte Carlo return-to-go samples for reward conditioning. In this work, we propose a novel approach that leverages the expressiveness of latent diffusion to model in-support trajectory sequences as compressed latent skills. This facilitates learning a Q-function while avoiding extrapolation error via batch-constraining. The latent space is also expressive and gracefully copes with multi-modal data. We show that the learned temporally-abstract latent space encodes richer task-specific information for offline RL tasks as compared to raw state-actions. This improves credit assignment and facilitates faster reward propagation during Q-learning. Our method demonstrates state-of-the-art performance on the D4RL benchmarks, particularly excelling in long-horizon, sparse-reward tasks.

Pixel-space generative models are often more difficult to train and generally underperform compared to their latent-space counterparts, leaving a persistent performance and efficiency gap. In this paper, we introduce a novel two-stage training framework that closes this gap for pixel-space diffusion and consistency models. In the first stage, we pre-train encoders to capture meaningful semantics from clean images while aligning them with points along the same deterministic sampling trajectory, which evolves points from the prior to the data distribution. In the second stage, we integrate the encoder with a randomly initialized decoder and fine-tune the complete model end-to-end for both diffusion and consistency models. Our training framework demonstrates strong empirical performance on ImageNet dataset. Specifically, our diffusion model reaches an FID of 2.04 on ImageNet-256 and 2.35 on ImageNet-512 with 75 number of function evaluations (NFE), surpassing prior pixel-space methods by a large margin in both generation quality and efficiency while rivaling leading VAE-based models at comparable training cost. Furthermore, on ImageNet-256, our consistency model achieves an impressive FID of 8.82 in a single sampling step, significantly surpassing its latent-space counterpart. To the best of our knowledge, this marks the first successful training of a consistency model directly on high-resolution images without relying on pre-trained VAEs or diffusion models.

Text-to-image diffusion models benefit artists with high-quality image generation. Yet its stochastic nature prevent artists from creating consistent images of the same character. Existing methods try to tackle this challenge and generate consistent content in various ways. However, they either depend on external data or require expensive tuning of the diffusion model. For this issue, we argue that a lightweight but intricate guidance is enough to function. Aiming at this, we lead the way to formalize the objective of consistent generation, derive a clustering-based score function and propose a novel paradigm, OneActor. We design a cluster-conditioned model which incorporates posterior samples to guide the denoising trajectories towards the target cluster. To overcome the overfitting challenge shared by one-shot tuning pipelines, we devise auxiliary components to simultaneously augment the tuning and regulate the inference. This technique is later verified to significantly enhance the content diversity of generated images. Comprehensive experiments show that our method outperforms a variety of baselines with satisfactory character consistency, superior prompt conformity as well as high image quality. And our method is at least 4 times faster than tuning-based baselines. Furthermore, to our best knowledge, we first prove that the semantic space has the same interpolation property as the latent space dose. This property can serve as another promising tool for fine generation control.

Variational autoencoders provide a principled framework for learning deep latent-variable models and corresponding inference models. In this work, we provide an introduction to variational autoencoders and some important extensions.

We introduce Latent Meaning Cells, a deep latent variable model which learns contextualized representations of words by combining local lexical context and metadata. Metadata can refer to granular context, such as section type, or to more global context, such as unique document ids. Reliance on metadata for contextualized representation learning is apropos in the clinical domain where text is semi-structured and expresses high variation in topics. We evaluate the LMC model on the task of zero-shot clinical acronym expansion across three datasets. The LMC significantly outperforms a diverse set of baselines at a fraction of the pre-training cost and learns clinically coherent representations. We demonstrate that not only is metadata itself very helpful for the task, but that the LMC inference algorithm provides an additional large benefit.

Autoregressive models have achieved impressive results over a wide range of domains in terms of generation quality and downstream task performance. In the continuous domain, a key factor behind this success is the usage of quantized latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for dimensionality reduction and faster inference times. However, using existing pre-trained models to perform new non-trivial tasks is difficult since it requires additional fine-tuning or extensive training to elicit prompting. This paper introduces LASS as a way to perform vector-quantized Latent Autoregressive Source Separation (i.e., de-mixing an input signal into its constituent sources) without requiring additional gradient-based optimization or modifications of existing models. Our separation method relies on the Bayesian formulation in which the autoregressive models are the priors, and a discrete (non-parametric) likelihood function is constructed by performing frequency counts over latent sums of addend tokens. We test our method on images and audio with several sampling strategies (e.g., ancestral, beam search) showing competitive results with existing approaches in terms of separation quality while offering at the same time significant speedups in terms of inference time and scalability to higher dimensional data.

Latent generative models have emerged as a leading approach for high-quality image synthesis. These models rely on an autoencoder to compress images into a latent space, followed by a generative model to learn the latent distribution. We identify that existing autoencoders lack equivariance to semantic-preserving transformations like scaling and rotation, resulting in complex latent spaces that hinder generative performance. To address this, we propose EQ-VAE, a simple regularization approach that enforces equivariance in the latent space, reducing its complexity without degrading reconstruction quality. By finetuning pre-trained autoencoders with EQ-VAE, we enhance the performance of several state-of-the-art generative models, including DiT, SiT, REPA and MaskGIT, achieving a 7 speedup on DiT-XL/2 with only five epochs of SD-VAE fine-tuning. EQ-VAE is compatible with both continuous and discrete autoencoders, thus offering a versatile enhancement for a wide range of latent generative models. Project page and code: https://eq-vae.github.io/.

We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models. We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples. Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences. We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.

The past several years have witnessed Variational Auto-Encoder's superiority in various text generation tasks. However, due to the sequential nature of the text, auto-regressive decoders tend to ignore latent variables and then reduce to simple language models, known as the KL vanishing problem, which would further deteriorate when VAE is combined with Transformer-based structures. To ameliorate this problem, we propose DELLA, a novel variational Transformer framework. DELLA learns a series of layer-wise latent variables with each inferred from those of lower layers and tightly coupled with the hidden states by low-rank tensor product. In this way, DELLA forces these posterior latent variables to be fused deeply with the whole computation path and hence incorporate more information. We theoretically demonstrate that our method can be regarded as entangling latent variables to avoid posterior information decrease through layers, enabling DELLA to get higher non-zero KL values even without any annealing or thresholding tricks. Experiments on four unconditional and three conditional generation tasks show that DELLA could better alleviate KL vanishing and improve both quality and diversity compared to several strong baselines.

Reasoning ability, a core component of human intelligence, continues to pose a significant challenge for Large Language Models (LLMs) in the pursuit of AGI. Although model performance has improved under the training scaling law, significant challenges remain, particularly with respect to training algorithms, such as catastrophic forgetting, and the limited availability of novel training data. As an alternative, test-time scaling enhances reasoning performance by increasing test-time computation without parameter updating. Unlike prior methods in this paradigm focused on token space, we propose leveraging latent space for more effective reasoning and better adherence to the test-time scaling law. We introduce LatentSeek, a novel framework that enhances LLM reasoning through Test-Time Instance-level Adaptation (TTIA) within the model's latent space. Specifically, LatentSeek leverages policy gradient to iteratively update latent representations, guided by self-generated reward signals. LatentSeek is evaluated on a range of reasoning benchmarks, including GSM8K, MATH-500, and AIME2024, across multiple LLM architectures. Results show that LatentSeek consistently outperforms strong baselines, such as Chain-of-Thought prompting and fine-tuning-based methods. Furthermore, our analysis demonstrates that LatentSeek is highly efficient, typically converging within a few iterations for problems of average complexity, while also benefiting from additional iterations, thereby highlighting the potential of test-time scaling in the latent space. These findings position LatentSeek as a lightweight, scalable, and effective solution for enhancing the reasoning capabilities of LLMs.

Large Language Models (LLMs) demonstrate their reasoning ability through chain-of-thought (CoT) generation. However, LLM's autoregressive decoding may limit the ability to revisit and refine earlier tokens in a holistic manner, which can also lead to inefficient exploration for diverse solutions. In this paper, we propose LaDiR (Latent Diffusion Reasoner), a novel reasoning framework that unifies the expressiveness of continuous latent representation with the iterative refinement capabilities of latent diffusion models for an existing LLM. We first construct a structured latent reasoning space using a Variational Autoencoder (VAE) that encodes text reasoning steps into blocks of thought tokens, preserving semantic information and interpretability while offering compact but expressive representations. Subsequently, we utilize a latent diffusion model that learns to denoise a block of latent thought tokens with a blockwise bidirectional attention mask, enabling longer horizon and iterative refinement with adaptive test-time compute. This design allows efficient parallel generation of diverse reasoning trajectories, allowing the model to plan and revise the reasoning process holistically. We conduct evaluations on a suite of mathematical reasoning and planning benchmarks. Empirical results show that LaDiR consistently improves accuracy, diversity, and interpretability over existing autoregressive, diffusion-based, and latent reasoning methods, revealing a new paradigm for text reasoning with latent diffusion.

The variational autoencoder (VAE) framework remains a popular option for training unsupervised generative models, especially for discrete data where generative adversarial networks (GANs) require workaround to create gradient for the generator. In our work modeling US postal addresses, we show that our discrete VAE with tree recursive architecture demonstrates limited capability of capturing field correlations within structured data, even after overcoming the challenge of posterior collapse with scheduled sampling and tuning of the KL-divergence weight beta. Worse, VAE seems to have difficulty mapping its generated samples to the latent space, as their VAE loss lags behind or even increases during the training process. Motivated by this observation, we show that augmenting training data with generated variants (augmented training) and training a VAE with multiple values of beta simultaneously (multiscale VAE) both improve the generation quality of VAE. Despite their differences in motivation and emphasis, we show that augmented training and multiscale VAE are actually connected and have similar effects on the model.

We propose L3DG, the first approach for generative 3D modeling of 3D Gaussians through a latent 3D Gaussian diffusion formulation. This enables effective generative 3D modeling, scaling to generation of entire room-scale scenes which can be very efficiently rendered. To enable effective synthesis of 3D Gaussians, we propose a latent diffusion formulation, operating in a compressed latent space of 3D Gaussians. This compressed latent space is learned by a vector-quantized variational autoencoder (VQ-VAE), for which we employ a sparse convolutional architecture to efficiently operate on room-scale scenes. This way, the complexity of the costly generation process via diffusion is substantially reduced, allowing higher detail on object-level generation, as well as scalability to large scenes. By leveraging the 3D Gaussian representation, the generated scenes can be rendered from arbitrary viewpoints in real-time. We demonstrate that our approach significantly improves visual quality over prior work on unconditional object-level radiance field synthesis and showcase its applicability to room-scale scene generation.

Large-scale pre-training tasks like image classification, captioning, or self-supervised techniques do not incentivize learning the semantic boundaries of objects. However, recent generative foundation models built using text-based latent diffusion techniques may learn semantic boundaries. This is because they have to synthesize intricate details about all objects in an image based on a text description. Therefore, we present a technique for segmenting real and AI-generated images using latent diffusion models (LDMs) trained on internet-scale datasets. First, we show that the latent space of LDMs (z-space) is a better input representation compared to other feature representations like RGB images or CLIP encodings for text-based image segmentation. By training the segmentation models on the latent z-space, which creates a compressed representation across several domains like different forms of art, cartoons, illustrations, and photographs, we are also able to bridge the domain gap between real and AI-generated images. We show that the internal features of LDMs contain rich semantic information and present a technique in the form of LD-ZNet to further boost the performance of text-based segmentation. Overall, we show up to 6% improvement over standard baselines for text-to-image segmentation on natural images. For AI-generated imagery, we show close to 20% improvement compared to state-of-the-art techniques. The project is available at https://koutilya-pnvr.github.io/LD-ZNet/.

We present a novel alignment-before-generation approach to tackle the challenging task of generating general 3D shapes based on 2D images or texts. Directly learning a conditional generative model from images or texts to 3D shapes is prone to producing inconsistent results with the conditions because 3D shapes have an additional dimension whose distribution significantly differs from that of 2D images and texts. To bridge the domain gap among the three modalities and facilitate multi-modal-conditioned 3D shape generation, we explore representing 3D shapes in a shape-image-text-aligned space. Our framework comprises two models: a Shape-Image-Text-Aligned Variational Auto-Encoder (SITA-VAE) and a conditional Aligned Shape Latent Diffusion Model (ASLDM). The former model encodes the 3D shapes into the shape latent space aligned to the image and text and reconstructs the fine-grained 3D neural fields corresponding to given shape embeddings via the transformer-based decoder. The latter model learns a probabilistic mapping function from the image or text space to the latent shape space. Our extensive experiments demonstrate that our proposed approach can generate higher-quality and more diverse 3D shapes that better semantically conform to the visual or textural conditional inputs, validating the effectiveness of the shape-image-text-aligned space for cross-modality 3D shape generation.

Generating time series data using Generative Adversarial Networks (GANs) presents several prevalent challenges, such as slow convergence, information loss in embedding spaces, instability, and performance variability depending on the series length. To tackle these obstacles, we introduce a robust framework aimed at addressing and mitigating these issues effectively. This advanced framework integrates the benefits of an Autoencoder-generated embedding space with the adversarial training dynamics of GANs. This framework benefits from a time series-based loss function and oversight from a supervisory network, both of which capture the stepwise conditional distributions of the data effectively. The generator functions within the latent space, while the discriminator offers essential feedback based on the feature space. Moreover, we introduce an early generation algorithm and an improved neural network architecture to enhance stability and ensure effective generalization across both short and long time series. Through joint training, our framework consistently outperforms existing benchmarks, generating high-quality time series data across a range of real and synthetic datasets with diverse characteristics.

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

Despite the extensive studies on Generative Adversarial Networks (GANs), how to reliably sample high-quality images from their latent spaces remains an under-explored topic. In this paper, we propose a novel GAN latent sampling method by exploring and exploiting the hubness priors of GAN latent distributions. Our key insight is that the high dimensionality of the GAN latent space will inevitably lead to the emergence of hub latents that usually have much larger sampling densities than other latents in the latent space. As a result, these hub latents are better trained and thus contribute more to the synthesis of high-quality images. Unlike the a posterior "cherry-picking", our method is highly efficient as it is an a priori method that identifies high-quality latents before the synthesis of images. Furthermore, we show that the well-known but purely empirical truncation trick is a naive approximation to the central clustering effect of hub latents, which not only uncovers the rationale of the truncation trick, but also indicates the superiority and fundamentality of our method. Extensive experimental results demonstrate the effectiveness of the proposed method.

Latent variable collaborative filtering methods have been a standard approach to modelling user-click interactions due to their simplicity and effectiveness. However, there is limited work on analyzing the mathematical properties of these methods in particular on preventing the overfitting towards the identity, and such methods typically utilize loss functions that overlook the geometry between items. In this work, we introduce a notion of generalization gap in collaborative filtering and analyze this with respect to latent collaborative filtering models. We present a geometric upper bound that gives rise to loss functions, and a way to meaningfully utilize the geometry of item-metadata to improve recommendations. We show how these losses can be minimized and gives the recipe to a new latent collaborative filtering algorithm, which we refer to as GeoCF, due to the geometric nature of our results. We then show experimentally that our proposed GeoCF algorithm can outperform other all existing methods on the Movielens20M and Netflix datasets, as well as two large-scale internal datasets. In summary, our work proposes a theoretically sound method which paves a way to better understand generalization of collaborative filtering at large.

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

Gaussian splatting typically requires dense observations of the scene and can fail to reconstruct occluded and unobserved areas. We propose a latent diffusion model to reconstruct a complete 3D scene with Gaussian splats, including the occluded parts, from only a single image during inference. Completing the unobserved surfaces of a scene is challenging due to the ambiguity of the plausible surfaces. Conventional methods use a regression-based formulation to predict a single "mode" for occluded and out-of-frustum surfaces, leading to blurriness, implausibility, and failure to capture multiple possible explanations. Thus, they often address this problem partially, focusing either on objects isolated from the background, reconstructing only visible surfaces, or failing to extrapolate far from the input views. In contrast, we propose a generative formulation to learn a distribution of 3D representations of Gaussian splats conditioned on a single input image. To address the lack of ground-truth training data, we propose a Variational AutoReconstructor to learn a latent space only from 2D images in a self-supervised manner, over which a diffusion model is trained. Our method generates faithful reconstructions and diverse samples with the ability to complete the occluded surfaces for high-quality 360-degree renderings.

Video-text retrieval is a class of cross-modal representation learning problems, where the goal is to select the video which corresponds to the text query between a given text query and a pool of candidate videos. The contrastive paradigm of vision-language pretraining has shown promising success with large-scale datasets and unified transformer architecture, and demonstrated the power of a joint latent space. Despite this, the intrinsic divergence between the visual domain and textual domain is still far from being eliminated, and projecting different modalities into a joint latent space might result in the distorting of the information inside the single modality. To overcome the above issue, we present a novel mechanism for learning the translation relationship from a source modality space S to a target modality space T without the need for a joint latent space, which bridges the gap between visual and textual domains. Furthermore, to keep cycle consistency between translations, we adopt a cycle loss involving both forward translations from S to the predicted target space T', and backward translations from T' back to S. Extensive experiments conducted on MSR-VTT, MSVD, and DiDeMo datasets demonstrate the superiority and effectiveness of our LaT approach compared with vanilla state-of-the-art methods.

Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have presented diffusion as an alternative to autoregressive language generation. We instead view diffusion as a complementary method that can augment the generative capabilities of existing pre-trained language models. We demonstrate that continuous diffusion models can be learned in the latent space of a pre-trained encoder-decoder model, enabling us to sample continuous latent representations that can be decoded into natural language with the pre-trained decoder. We show that our latent diffusion models are more effective at sampling novel text from data distributions than a strong autoregressive baseline and also enable controllable generation.

Consistency models are a new family of generative models capable of producing high-quality samples in either a single step or multiple steps. Recently, consistency models have demonstrated impressive performance, achieving results on par with diffusion models in the pixel space. However, the success of scaling consistency training to large-scale datasets, particularly for text-to-image and video generation tasks, is determined by performance in the latent space. In this work, we analyze the statistical differences between pixel and latent spaces, discovering that latent data often contains highly impulsive outliers, which significantly degrade the performance of iCT in the latent space. To address this, we replace Pseudo-Huber losses with Cauchy losses, effectively mitigating the impact of outliers. Additionally, we introduce a diffusion loss at early timesteps and employ optimal transport (OT) coupling to further enhance performance. Lastly, we introduce the adaptive scaling-c scheduler to manage the robust training process and adopt Non-scaling LayerNorm in the architecture to better capture the statistics of the features and reduce outlier impact. With these strategies, we successfully train latent consistency models capable of high-quality sampling with one or two steps, significantly narrowing the performance gap between latent consistency and diffusion models. The implementation is released here: https://github.com/quandao10/sLCT/