Variational Autoencoders

Also known as VAE

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Variational autoencoders learn probability distributions over compact latent codes and decode samples from them, typically by balancing reconstruction quality against a KL-divergence regularizer in the evidence lower bound. Common approaches use Gaussian, mixture, flow-based, spherical, or heavy-tailed priors, and add hierarchical, disentangling, temporal, multimodal, geometric, or physics-informed structure. They are used for image, video, audio, molecule, medical, and scientific data, both as generative models and as compact representations for downstream prediction or diffusion. A central tension is that stronger regularization can make generation easier while causing posterior collapse or losing useful detail; reconstruction scores alone also do not guarantee good samples, calibrated uncertainty, or useful latent structure.

Latest papers

210 papers30 papers in the last four weeks, up 131% on the four weeks before. 0.2% of all new papers.

Mar 1, 2026

Time-Aware Latent Space Bayesian Optimization

Latent-space Bayesian optimization (LSBO) extends Bayesian optimization to structured domains, such as molecular design, by searching in the continuous latent space of a generative model. However, most LSBO methods assume a fixed objective, whereas real design campaigns often face temporal drift (e.g., evolving preferences or shifting targets). Bringing time-varying BO into LSBO is nontrivial: drift can affect not only the surrogate, but also the latent search space geometry induced by the representation. We propose Time-Aware Latent-space Bayesian Optimization (TALBO), which incorporates time in both the surrogate and the learned generative representation via a GP-prior variational autoencoder, yielding a latent space aligned as objectives evolve. To evaluate timevarying LSBO systematically, we adapt widely used molecular design tasks to drifting multi-property objectives and introduce metrics tailored to changing targets. Across these benchmarks, TALBO consistently outperforms strong LSBO baselines and remains robust across drift speeds and design choices, while remaining competitive under actually time-invariant objectives.

Tuan A. Vu, Julien Martinelli, Harri Lähdesmäki

Aalto University

Molecule Design Bayesian Optimization Latent Space Optimization Variational Autoencoders

Feb 28, 2026

Data-driven Synthesis of Magnetic Resonance Spectroscopy Data using a Variational Autoencoder

The development of deep learning methods for magnetic resonance spectroscopy (MRS) is often hindered by limited availability of large, high-quality training datasets. While physics-based simulations are commonly used to mitigate this limitation, accurately modeling all in-vivo signal components remains challenging. In this work, we propose a data-driven framework for synthesizing in-vivo MRS data using a variational autoencoder (VAE) trained exclusively on measured single-voxel spectroscopy data. The model learns a low-dimensional latent representation of complex-valued spectra and enables generation of new samples through latent-space sampling and interpolation. The generative performance of the proposed approach is evaluated using a comprehensive set of complementary analyses, including reconstruction quality, feature-level similarity using low-dimensional embeddings, application-based signal quality metrics, and metabolite quantification agreement. The results demonstrate that the VAE accurately reconstructs dominant spectral patterns and generates synthetic spectra that occupy the same feature space as in-vivo data. In an example application targeting GABA-edited spectroscopy, augmenting limited subsets of transients with synthetic spectra improves signal quality metrics such as signal-to-noise ratio, linewidth, and shape scores. However, the results also reveal limitations of the generative approach, including under-representation of stochastic noise and reduced accuracy in absolute metabolite quantification, particularly for applications sensitive to concentration estimates. These findings highlight both potential and limitations of data-driven MRS synthesis. Beyond the proposed model, this study introduces a structured evaluation framework for generative MRS methods, emphasizing the importance of application-aware validation when synthetic data are used for downstream analysis.

Dennis M. J. van de Sande, Julian P. Merkofer, Sina Amirrajab +4

Department of Biomedical Engineering Eindhoven University of Technology Eindhoven, The Netherlands · Department of Electrical Engineering Eindhoven University of Technology Eindhoven, The Netherlands · Department of Radiology & Nuclear Medicine Maastricht University Medical Center Maastricht, The Netherlands

Magnetic Resonance Spectroscopy Synthetic Data Generation Synthetic Data Evaluation Variational Autoencoders

Feb 26, 2026

Latent Matters: Learning Deep State-Space Models

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model actually learns the underlying dynamics. We therefore propose a constrained optimisation framework as a general approach for training DSSMs. Building upon this, we introduce the extended Kalman VAE (EKVAE), which combines amortised variational inference with classic Bayesian filtering/smoothing to model dynamics more accurately than RNN-based DSSMs. Our results show that the constrained optimisation framework significantly improves system identification and prediction accuracy on the example of established state-of-the-art DSSMs. The EKVAE outperforms previous models w.r.t. prediction accuracy, achieves remarkable results in identifying dynamical systems, and can furthermore successfully learn state-space representations where static and dynamic features are disentangled.

Alexej Klushyn, Richard Kurle, Maximilian Soelch +2

Technical University of Munich · AWS AI Labs · Machine Learning Research Lab, Volkswagen Group, Munich +1

State Space Models Latent Dynamics Modeling Variational Autoencoders System Identification State Representation Learning

Feb 24, 2026

Disentangled Hierarchical VAE for 3D Human-Human Interaction Generation

Generating realistic 3D Human-Human Interaction (HHI) requires coherent modeling of the physical plausibility of the agents and their interaction semantics. Existing methods compress all motion information into a single latent representation, limiting their ability to capture fine-grained actions and inter-agent interactions. This often leads to semantic misalignment and physically implausible artifacts, such as penetration or missed contact. We propose Disentangled Hierarchical Variational Autoencoder (DHVAE) based latent diffusion for structured and controllable HHI generation. DHVAE explicitly disentangles the global interaction context and individual motion patterns into a decoupled latent structure by employing a CoTransformer module. To mitigate implausible and physically inconsistent contacts in HHI, we incorporate contrastive learning constraints with our DHVAE to promote a more discriminative and physically plausible latent interaction space. For high-fidelity interaction synthesis, DHVAE employs a DDIM-based diffusion denoising process in the hierarchical latent space, enhanced by a skip-connected AdaLN-Transformer denoiser. Extensive evaluations show that DHVAE achieves superior motion fidelity, text alignment, and physical plausibility with greater computational efficiency.

Zichen Geng, Zeeshan Hayder, Bo Miao +3

Department of CSSE, The University of Western Australia, Crawley WA 6009, Australia · Data61, CSIRO, Acton ACT 2601, Australia · Australian Institute for Machine Learning, The University of Adelaide, Adelaide SA 5000, Australia +1

Human Motion Generation Variational Autoencoders Diffusion Models for Motion Generation Disentangled Representation Learning

Feb 24, 2026

VAE-MS: An Asymmetric Variational Autoencoder for Mutational Signature Extraction

Mutational signature analysis has emerged as a powerful method for uncovering the underlying biological processes driving cancer development. However, the signature extraction process, typically performed using non-negative matrix factorization (NMF), often lacks reliability and clinical applicability. To address these limitations, several solutions have been introduced, including the use of neural networks to achieve more accurate estimates and probabilistic methods to better capture natural variation in the data. In this work, we introduce a Variational Autoencoder for Mutational Signatures (VAE-MS), a novel model that leverages both an asymmetric architecture and probabilistic methods for the extraction of mutational signatures. VAE-MS is compared to with three state-of-the-art models for mutational signature extraction: SigProfilerExtractor, the NMF-based gold standard; MUSE-XAE, an autoencoder that employs an asymmetric design without probabilistic components; and SigneR, a Bayesian NMF model, to illustrate the strength in combining a nonlinear extraction with a probabilistic model. In the ability to reconstruct input data and generalize to unseen data, models with probabilistic components (VAE-MS, SigneR) dramatically outperformed models without (SigProfilerExtractor, MUSE-XAE). The NMF-baed models (SigneR, SigProfilerExtractor) had the most accurate reconstructions in simulated data, while VAE-MS reconstructed more accurately on real cancer data. Upon evaluating the ability to extract signatures consistently, no model exhibited a clear advantage over the others. Software for VAE-MS is available at https://github.com/CLINDA-AAU/VAE-MS.

Ida Egendal, Rasmus Froberg Brøndum, Dan J Woodcock +2

Center for Clinical Data Science, Aalborg University and Aalborg University Hospital, Aalborg, 9260, Denmark. · Clinical Cancer Research Center, Aalborg University Hospital, Aalborg, 9000, Denmark. · Nuffield Department of Surgical Sciences, University of Oxford, Oxford, OX3 9DU, England. +1

Cancer Genomics Variational Autoencoders

Feb 23, 2026

Unsupervised Anomaly Detection in NSL-KDD Using $β$ -VAE: A Latent Space and Reconstruction Error Approach

As Operational Technology increasingly integrates with Information Technology, the need for Intrusion Detection Systems becomes more important. This paper explores an unsupervised approach to anomaly detection in network traffic using

β

-Variational Autoencoders on the NSL-KDD dataset. We investigate two methods: leveraging the latent space structure by measuring distances from test samples to the training data projections, and using the reconstruction error as a conventional anomaly detection metric. By comparing these approaches, we provide insights into their respective advantages and limitations in an unsupervised setting. Experimental results highlight the effectiveness of latent space exploitation for classification tasks.

Dylan Baptiste, Ramla Saddem, Alexandre Philippot +1

CRESTIC · Université de Reims Champagne-Ardenne, CRESTIC, Reims, France · Seckiot, Paris, France

Unsupervised Anomaly Detection Network Intrusion Detection Reconstruction-Based Anomaly Detection Variational Autoencoders

Feb 22, 2026

Flash-VAED: Plug-and-Play VAE Decoders for Efficient Video Generation

Latent diffusion models have enabled high-quality video synthesis, yet their inference remains costly and time-consuming. As diffusion transformers become increasingly efficient, the latency bottleneck inevitably shifts to VAE decoders. To reduce their latency while maintaining quality, we propose a universal acceleration framework for VAE decoders that preserves full alignment with the original latent distribution. Specifically, we propose (1) an independence-aware channel pruning method to effectively mitigate severe channel redundancy, and (2) a stage-wise dominant operator optimization strategy to address the high inference cost of the widely used causal 3D convolutions in VAE decoders. Based on these innovations, we construct a Flash-VAED family. Moreover, we design a three-phase dynamic distillation framework that efficiently transfers the capabilities of the original VAE decoder to Flash-VAED. Extensive experiments on Wan and LTX-Video VAE decoders demonstrate that our method outperforms baselines in both quality and speed, achieving approximately a 6

\times

speedup while maintaining the reconstruction performance up to 96.9%. Notably, Flash-VAED accelerates the end-to-end generation pipeline by up to 36% with negligible quality drops on VBench-2.0. Our code is available at https://github.com/Aoko955/Flash-VAED.

Lunjie Zhu, Yushi Huang, Xingtong Ge +5

iComAI Lab, Hong Kong University of Science and Technology, Hong Kong SAR, China · School of Data Science, Lingnan University, Hong Kong SAR, China

Channel Pruning Variational Autoencoders Video Diffusion Models Structured Pruning

Feb 21, 2026

PCA-VAE: Differentiable Subspace Quantization without Codebook Collapse

Vector-quantized autoencoders deliver high-fidelity latents but suffer inherent flaws: the quantizer is non-differentiable, requires straight-through hacks, and is prone to collapse. We address these issues at the root by replacing VQ with a simple, principled, and fully differentiable alternative: an online PCA bottleneck trained via Oja's rule. The resulting model, PCA-VAE, learns an orthogonal, variance-ordered latent basis without codebooks, commitment losses, or lookup noise. Despite its simplicity, PCA-VAE exceeds VQ-GAN and SimVQ in reconstruction quality on CelebAHQ while using 10-100x fewer latent bits. It also produces naturally interpretable dimensions (e.g., pose, lighting, gender cues) without adversarial regularization or disentanglement objectives. These results suggest that PCA is a viable replacement for VQ: mathematically grounded, stable, bit-efficient, and semantically structured, offering a new direction for generative models beyond vector quantization.

Hao Lu, Onur C. Koyun, Yongxin Guo +3

Wake Forest University School of Medicine, Winston-Salem, NC, USA

Vector Quantization Vector-Quantized Variational Autoencoder Variational Autoencoders Principal Component Analysis

Feb 20, 2026

Variational Distributional Neuron

We propose a proof of concept for a variational distributional neuron: a compute unit formulated as a VAE brick, explicitly carrying a prior, an amortized posterior and a local ELBO. The unit is no longer a deterministic scalar but a distribution: computing is no longer about propagating values, but about contracting a continuous space of possibilities under constraints. Each neuron parameterizes a posterior, propagates a reparameterized sample and is regularized by the KL term of a local ELBO - hence, the activation is distributional. This "contraction" becomes testable through local constraints and can be monitored via internal measures. The amount of contextual information carried by the unit, as well as the temporal persistence of this information, are locally tuned by distinct constraints. This proposal addresses a structural tension: in sequential generation, causality is predominantly organized in the symbolic space and, even when latents exist, they often remain auxiliary, while the effective dynamics are carried by a largely deterministic decoder. In parallel, probabilistic latent models capture factors of variation and uncertainty, but that uncertainty typically remains borne by global or parametric mechanisms, while units continue to propagate scalars - hence the pivot question: if uncertainty is intrinsic to computation, why does the compute unit not carry it explicitly? We therefore draw two axes: (i) the composition of probabilistic constraints, which must be made stable, interpretable and controllable; and (ii) granularity: if inference is a negotiation of distributions under constraints, should the primitive unit remain deterministic or become distributional? We analyze "collapse" modes and the conditions for a "living neuron", then extend the contribution over time via autoregressive priors over the latent, per unit.

Yves Ruffenach

Conservatoire National des Arts et Métiers

Variational Autoencoders Variational Inference

Feb 18, 2026

HiVAE: Hierarchical Latent Variables for Scalable Theory of Mind

Theory of mind (ToM) enables AI systems to infer agents' hidden goals and mental states, but existing approaches focus mainly on small human understandable gridworld spaces. We introduce HiVAE, a hierarchical variational architecture that scales ToM reasoning to realistic spatiotemporal domains. Inspired by the belief-desire-intention structure of human cognition, our three-level VAE hierarchy achieves substantial performance improvements on a 3,185-node campus navigation task. However, we identify a critical limitation: while our hierarchical structure improves prediction, learned latent representations lack explicit grounding to actual mental states. We propose self-supervised alignment strategies and present this work to solicit community feedback on grounding approaches.

Nigel Doering, Rahath Malladi, Arshia Sangwan +2

University of California San Diego, School of Computing, Information, and Data Sciences · New York University · University of Virginia

Theory of Mind Cognitive Architectures for AI Agents Variational Autoencoders Latent Space Alignment

Feb 18, 2026

Cryo-SWAN: the Multi-Scale Wavelet-decomposition-inspired Autoencoder Network for molecular density representation of molecular volumes

Learning robust representations of 3D shapes from voxelized data is essential for advancing AI methods in biomedical imaging. However, most contemporary 3D computer vision approaches operate on point clouds, meshes, or octrees, while volumetric density maps, the native format of structural biology and cryo-EM, remain comparatively underexplored. We present Cryo-SWAN, a voxel-based variational autoencoder inspired by multi-scale wavelet decomposition. The model performs conditional coarse-to-fine latent encoding and recursive residual quantization across perception scales, enabling accurate capture of both global geometry and high-frequency structural detail in molecular density volumes. Evaluated on ModelNet40, BuildingNet, and a newly curated dataset of cryo-EM volumes, ProteinNet3D, Cryo-SWAN consistently improves reconstruction quality over state-of-the-art 3D autoencoders. We demonstrate that the molecular densities organize in learned latent space according to shared geometric features, while integration with diffusion models enables denoising and conditional shape generation. Together, Cryo-SWAN is a practical framework for data-driven structural biology and volumetric imaging.

Rui Li, Artsemi Yushkevich, Mikhail Kudryashev +1

Center for Advanced Systems Understanding (CASUS), Görlitz, Germany. · Helmholtz-Zentrum Dresden-Rossendorf e. V. (HZDR), Dresden, Germany. · In situ Structural Biology, Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany. +4

3D Representation Learning Molecular Representation Learning Variational Autoencoders Cryo-Electron Microscopy

Feb 3, 2026

Multiparameter Uncertainty Mapping in Quantitative Molecular MRI using a Physics-Structured Variational Autoencoder (PS-VAE)

Quantitative imaging methods, such as magnetic resonance fingerprinting (MRF), aim to extract interpretable pathology biomarkers by estimating biophysical tissue parameters from signal evolutions. However, the pattern-matching algorithms or neural networks used in such inverse problems often lack principled uncertainty quantification, which limits the trustworthiness and transparency, required for clinical acceptance. Here, we describe a physics-structured variational autoencoder (PS-VAE) designed for rapid extraction of voxelwise multi-parameter posterior distributions. Our approach integrates a differentiable spin physics simulator with self-supervised learning, and provides a full covariance that captures the inter-parameter correlations of the latent biophysical space. The method was validated in a multi-proton pool chemical exchange saturation transfer (CEST) and semisolid magnetization transfer (MT) molecular MRF study, across in-vitro phantoms, tumor-bearing mice, healthy human volunteers, and a subject with glioblastoma. The resulting multi-parametric posteriors are in good agreement with those calculated using a brute-force Bayesian analysis, while providing an orders-of-magnitude acceleration in whole brain quantification. In addition, we demonstrate how monitoring the multi-parameter posterior dynamics across progressively acquired signals provides practical insights for protocol optimization and may facilitate real-time adaptive acquisition.

Alex Finkelstein, Ron Moneta, Or Zohar +4

School of Biomedical Engineering, Tel-Aviv University, Tel-Aviv, Israel · Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv, Israel · School of Biochemistry, Neurobiology, and Biophysics, Tel-Aviv University, Tel-Aviv, Israel +1

Magnetic Resonance Imaging Uncertainty Quantification Physics-Informed Generative Modeling Variational Autoencoders Neural Posterior Estimation

Feb 3, 2026

Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification

Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but interpretable uncertainty. Providing fast inference alongside uncertainty estimates remains challenging yet desirable in numerous applications. We propose the Variational Sparse Paired Autoencoder (vsPAIR) to address this challenge. The architecture pairs a standard VAE encoding observations with a sparse VAE encoding quantities of interest (QoI), connected through a learned latent mapping. The variational structure enables uncertainty estimation, the paired architecture encourages interpretability by anchoring QoI representations to clean data, and sparse encodings provide structure by concentrating information into identifiable factors rather than diffusing across all dimensions. To validate the effectiveness of our proposed architecture, we conduct experiments on blind inpainting, computed tomography (CT), and initial-condition inference for the heat equation, demonstrating that vsPAIR is a capable inverse problem solver that can provide interpretable and structured uncertainty estimates.

Jack Michael Solomon, Rishi Leburu, Matthias Chung

Emory University Department of Mathematics

Variational Autoencoders Uncertainty Quantification Autoencoders Sparse Autoencoders Inverse Problems

Jan 29, 2026

XFACTORS: Disentangled Information Bottleneck via Contrastive Supervision

Disentangled representation learning aims to map independent factors of variation to independent representation components. On one hand, purely unsupervised approaches have proven successful on fully disentangled synthetic data, but fail to recover semantic factors from real data without strong inductive biases. On the other hand, supervised approaches are unstable and hard to scale to large attribute sets because they rely on adversarial objectives or auxiliary classifiers. We introduce XFactors, a weakly-supervised VAE framework that disentangles and provides explicit control over a chosen set of factors. Building on the Disentangled Information Bottleneck perspective, we decompose the representation into a residual subspace

\mathcal{S}

and factor-specific subspaces

\mathcal{T}_1,\ldots,\mathcal{T}_K

and a residual subspace

\mathcal{S}

. Each target factor is encoded in its assigned

\mathcal{T}_i

through contrastive supervision: an InfoNCE loss pulls together latents sharing the same factor value and pushes apart mismatched pairs. In parallel, KL regularization imposes a Gaussian structure on both

\mathcal{S}

and the aggregated factor subspaces, organizing the geometry without additional supervision for non-targeted factors and avoiding adversarial training and classifiers. Across multiple datasets, with constant hyperparameters, XFactors achieves state-of-the-art disentanglement scores and yields consistent qualitative factor alignment in the corresponding subspaces, enabling controlled factor swapping via latent replacement. We further demonstrate that our method scales correctly with increasing latent capacity and evaluate it on the real-world dataset CelebA. Our code is available at github.com/ICML26-anon/XFactors.

Alexandre Myara, Nicolas Bourriez, Thomas Boyer +3

ENS Paris

Variational Autoencoders Disentangled Representation Learning Information Bottleneck Variational Information Bottleneck

Jan 20, 2026

VENI: Variational Encoder for Natural Illumination

Inverse rendering is an ill-posed problem, but priors such as illumination priors can help simplify it. Existing work either disregards the spherical and rotation-equivariant nature of illumination environments or does not provide a well-behaved latent space. We propose a rotation-equivariant variational autoencoder that models natural illumination on the sphere without relying on 2D projections. To preserve the SO(2)-equivariance of environment maps, we use a novel Vector Neuron Vision Transformer (VN-ViT) as encoder and a rotation-equivariant conditional neural field as decoder. In the encoder, we reduce the equivariance from SO(3) to SO(2) using a novel SO(2)-equivariant fully connected layer, an extension of Vector Neurons. We show that our SO(2)-equivariant fully connected layer outperforms standard Vector Neurons when used in our SO(2)-equivariant model. Compared to previous methods, our variational autoencoder enables smoother interpolation in latent space and offers a more well-behaved latent space.

Paul Walker, James A. D. Gardner, Andreea Ardelean +2

Friedrich-Alexander-Universität Erlangen-Nürnberg · University of York

Variational Autoencoders Inverse Rendering Equivariant Neural Networks

Dec 28, 2025

QSAR-Guided Generative Framework for the Discovery of Synthetically Viable Odorants

The discovery of novel odorant molecules is key for the fragrance and flavor industries, yet efficiently navigating the vast chemical space to identify structures with desirable olfactory properties remains a significant challenge. Generative artificial intelligence offers a promising approach for de novo molecular design but typically requires large sets of molecules to learn from. To address this problem, we present a framework combining a variational autoencoder (VAE) with a quantitative structure-activity relationship (QSAR) model to generate novel odorants from limited training sets of odor molecules. The self-supervised learning capabilities of the VAE allow it to learn SMILES grammar from ChEMBL database, while its training objective is augmented with a loss term derived from an external QSAR model to structure the latent representation according to odor probability. While the VAE demonstrated high internal consistency in learning the QSAR supervision signal, validation against an external, unseen ground truth dataset (Unique Good Scents) confirms the model generates syntactically valid structures (100% validity achieved via rejection sampling) and 93.9% unique structures. The latent space is effectively structured by odor likelihood, evidenced by a Frechet ChemNet Distance (FCD) of ~6.96 between generated molecules and known odorants, compared to ~21.6 for the ChEMBL baseline. An ablation of the property head shows that its contribution lies in the density of retrievable structures near an odorant seed -- a 4.3-fold increase in distinct novel compounds per seed -- rather than in the odor-likeness of any individual compound. Bemis-Murcko analysis shows 2,499 of 6,765 ring-containing candidates, spanning 1,429 distinct core frameworks, absent from all training sets, while a further 294 molecules...

Tim C. Pearce, Ahmed Ibrahim

Biomedical Engineering Research Group, School of Engineering, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom · School of Clinical Medicine, University of Cambridge, Addenbrooke’s Hospital, Hills Road, Cambridge CB2 0SP, United Kingdom

Molecular Generation Variational Autoencoders

Dec 8, 2025

Distribution Matching Variational AutoEncoder

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.

Sen Ye, Jianning Pei, Mengde Xu +4

State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University · University of Chinese Academy of Sciences · Tencent +1

Variational Autoencoders Generative Modeling

Dec 7, 2025

Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions

Score-based generative models commonly employ linear forward diffusions with Gaussian reference distributions, limiting their ability to directly incorporate structural information into the noising dynamics. We introduce latent nonlinear denoising score matching (LNDSM), which combines nonlinear, structure-informed latent diffusions with the variational autoencoder (VAE) training framework. In our construction, the forward diffusion is designed to admit a prescribed reference distribution, such as a Gaussian mixture model, that reflects qualitative features of the latent data distribution. We derive a computable approximation to a cross-entropy upper bound in the VAE objective using Euler-Maruyama discretization and the resulting Gaussian conditional transitions. To stabilize training, we remove two zero-mean control variates whose variances become large for small time steps. The resulting objective enables joint training of the encoder, decoder, and latent score network. Numerical experiments on benchmark image datasets demonstrate the effectiveness of LNDSM in learning structured distributions, outperforming conventional latent score-based generative modeling in sample quality and mode balance across several settings, while achieving improved training efficiency. These results highlight the potential of nonlinear, structure-informed latent diffusions for generative modeling.

Kaichen Shen, Wei Zhu

School of Mathematics, Georgia Institute of Technology, Atlanta, GA

Score-Based Generative Modeling Diffusion Models Latent Diffusion Models Variational Autoencoders

Dec 5, 2025

Delving into Latent Spectral Biasing of Video VAEs for Superior Diffusability

Latent diffusion models pair VAEs with diffusion backbones, and the structure of VAE latents strongly influences the difficulty of diffusion training. However, existing video VAEs typically focus on reconstruction fidelity, overlooking latent structure. We present a statistical analysis of video VAE latent spaces and identify two spectral properties essential for diffusion training: a spatio-temporal frequency spectrum biased toward low frequencies, and a channel-wise eigenspectrum dominated by a few modes. To induce these properties, we propose two lightweight, backbone-agnostic regularizers: Local Correlation Regularization and Latent Masked Reconstruction. Experiments show that our Spectral-Structured VAE (SSVAE) achieves a

3\times

speedup in text-to-video generation convergence and a 10% gain in video reward, outperforming strong open-source VAEs. The code is available at https://github.com/zai-org/SSVAE.

Shizhan Liu, Xinran Deng, Zhuoyi Yang +3

Zhipu AI, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Tsinghua University, Beijing, China

Variational Autoencoders Spectral Regularization Video Diffusion Models Latent Diffusion Models

Oct 17, 2025

Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization

Bayesian optimisation (BO) enables sample-efficient global optimisation of expensive black-box functions but remains challenging in high dimensions. We investigate nonlinear dimensionality reduction to a sequence of low-dimensional latent-space BO (LSBO) problems. Early LSBO used linear random and supervised embeddings; building on Grosnit et al., we employ variational autoencoders (VAEs), deep metric loss for structured latent manifolds, and retraining to adapt the encoder-decoder pair to newly sampled regions. We couple LSBO with sequential domain reduction (SDR) directly in latent space (SDR-LSBO), narrowing search domains as evidence accumulates. Implemented in GPU-accelerated BoTorch with Mat'ern-5/2 Gaussian-process surrogates, our methods improve benchmark optimisation quality, and retraining can enhance BO performance. Comparisons with adaptive supervised linear random embeddings demonstrate the effectiveness of VAE-based BO for nonlinear low-dimensional structures. We analyse BO-VAE with a fixed pretrained representation, decomposing ambient-space simple regret into latent BO error and a fixed VAE-induced representation gap. Under a PAC-Bayes-certified reconstruction condition and standard fixed-prior assumptions for expected improvement with a Mat'ern-5/2 kernel, latent BO error vanishes as the evaluation budget increases, whereas the representation gap remains fixed and may impose a non-vanishing error floor. Visualisations empirically assess accessibility of the ambient optimum through the learned decoder. To our knowledge, this is the first study combining SDR with VAE-based LSBO. Our analysis clarifies metric shaping and retraining choices critical for scalable latent-space BO. For reproducibility, source code is available at https://github.com/L-Lok/Nonlinear-Dimensionality-Reduction-Techniques-for-Bayesian-Optimization.git.

Luo Long, Coralia Cartis, Paz Fink Shustin

Mathematical Institute, University of Oxford, Radcliffe Observatory, Andrew Wiles Building, Woodstock Rd, Oxford, OX2 6GG, United Kingdom.

Variational Autoencoders Bayesian Optimization Dimensionality Reduction Latent Space Optimization

Sep 28, 2025

Latent Representation Learning from 3D Brain MRI for Latent Analysis and Prediction in Multiple Sclerosis

Neurological diseases can cause significant cognitive impairment, yet linking brain structure to cognitive function remains challenging due to the limitations of conventional methods and the black-box nature of deep learning. We propose InfoVAE-Med3D, an adaptation of InfoVAE for three-dimensional brain MRI that learns informative latent representations by relaxing the mutual information regularization penalty between inputs and latent representations. We evaluated the method on a healthy control (HC) dataset (

n=6{,}503

) with age and sex information and a multiple sclerosis (MS) dataset (

n=916

) with age, sex, and Symbol Digit Modalities Test (SDMT) scores. Two-dimensional visualizations revealed sex-related clustering and smooth transitions in grey and white matter volumes. Removing the mutual information regularization penalty generally improved MRI reconstruction and brain age and SDMT prediction using support vector regression, outperforming other variational autoencoder variants and achieving competitive performance with deep learning predictors, particularly on the MS dataset. InfoVAE-Med3D provides informative latent representations for investigating brain-related characteristics and supports latent-space analysis and imaging biomarker discovery for cognitive impairment, particularly in MS.

Trinh Ngoc Huynh, Nguyen Duc Kien, Nguyen Hai Anh +8

VNU University of Engineering and Technology, Hanoi, Vietnam. · Bach Mai Hospital, Hanoi, Vietnam. · Department of Radiology, First Faculty of Medicine, Charles University, General University Hospital, Prague, Czech Republic. +3

Medical Image Representation Learning Variational Autoencoders Brain MRI Latent-Space Regularization

Aug 16, 2025

DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy

Recently, autoencoders (AEs) have gained interest for creating parametric and invertible projections of multidimensional data. Parametric projections make it possible to embed new, unseen samples without recalculating the entire projection, while invertible projections allow the synthesis of new data instances. However, existing methods perform poorly when dealing with out-of-distribution samples in either the data or embedding space. Thus, we propose DE-VAE, an uncertainty-aware variational AE using differential entropy (DE) to improve the learned parametric and invertible projections. Given a fixed projection, we train DE-VAE to learn a mapping into 2D space and an inverse mapping back to the original space. We conduct quantitative and qualitative evaluations on four well-known datasets, using UMAP and t-SNE as baseline projection methods. Our findings show that DE-VAE can create parametric and inverse projections with comparable accuracy to other current AE-based approaches while enabling the analysis of embedding uncertainty.

Frederik L. Dennig, Daniel A. Keim

University of Konstanz

Variational Autoencoders Uncertainty Quantification OOD Generalization Inverse Dimensionality Reduction Dimensionality Reduction

Jul 31, 2025

L-GTA: Latent Generative Modeling for Time Series Augmentation

Data augmentation is becoming increasingly important across various areas of time series analysis, including forecasting, classification, and anomaly detection. We introduce the Latent Generative Temporal Augmentation (L-GTA) model, a generative approach based on a Variational Autoencoder with a Bi-LSTM backbone and temporal self-attention. The model learns a latent representation for each timestep and applies controlled perturbations such as jittering, magnitude warping, or drift. We define an equivariance objective to further encourage consistency between latent space and data space transformations. As a result, the augmented samples show predictable and interpretable transformation signatures. We evaluate L-GTA on several real-world datasets against SOTA generative methods, including TimeGAN, TimeVAE, and Diffusion-TS, as well as direct transformation approaches. Across experiments on downstream forecasting, distribution fidelity, and controllability of transformation intensity, L-GTA consistently outperforms competing approaches. In downstream forecasting, it reduces prediction error by up to 26% compared to the strongest generative method and 27% relative to using the original data without augmentation.

Luis Roque, Vitor Cerqueira, Carlos Soares +1

Faculdade de Engenharia da Universidade do Porto, Porto, Portugal · University of Coimbra, Coimbra, Portugal · Fraunhofer Portugal AICOS, Portugal +1

Variational Autoencoders Synthetic Data Augmentation Representation Learning Time Series Data Augmentation Equivariant Representation Learning

Jun 26, 2025

Spherical Cauchy Variational Autoencoders: Heavy Angular Tails and Exact KL Evaluation

Heavy-tailed posteriors are routine in Euclidean variational autoencoders, where the Student family relaxes the Gaussian without new machinery. The sphere has had no comparable option. Von Mises-Fisher distribution needs modified Bessel functions and a rejection sampler, and Power Spherical buys its closed forms by forcing the density to vanish at the antipode. We develop the spherical Cauchy distribution as a hyperspherical posterior that needs neither compromise. Stereographic projection carries it to a multivariate Student law, and a Möbius transformation turns a uniform spherical draw into an exact posterior sample from inner products, norms, and scalar arithmetic. The same transformation settles the regularizer. Evaluating the density along the sampling map reduces the Kullback-Leibler (KL) divergence to the uniform prior to a scalar expectation whose expansion terminates in every even ambient dimension, leaving one logarithm and a polynomial with finitely many correction terms. Odd dimensions admit certified truncation of value and gradient, the KL is increasing and convex in concentration, and the same function gives the pairwise KL. At matched modal curvature it has broader angular tails and a smaller KL penalty than both alternatives, so equal local precision costs less regularization. In dimension 128 the fused evaluator runs 1.5 times faster per latent-layer step than Power Spherical and 4.2 times faster than robust von Mises-Fisher on CPU, with factors of 1.6 and 5.4 on CUDA. Across five paired seeds it attains the lowest MNIST reconstruction loss at every tested dimension and lowers held-out viewpoint-gap negative log-likelihood on smallNORB by 3.6 percent.

Lukas Sablica, Kurt Hornik

Institute for Statistics and Mathematics Vienna University of Economics and Business Austria

Variational Autoencoders Hyperspherical Representation Learning Heavy-Tailed Distributions

Jun 24, 2025

Cross-Layer Discrete Concept Discovery for Interpreting Language Models

Interpreting language models remains challenging due to the existence of residual stream, which linearly mixes and duplicates features across adjacent layers, causing single-layer analyses to miss this cross-layer structure. Cross-layer sparse autoencoders (SAEs) address layer mixing but operate in continuous space, where concepts split across many neurons without clear boundaries. We introduce Cross-Layer Vector Quantized-Variational Autoencoder (CLVQ-VAE), a novel framework which maps representations from a lower layer to a higher layer through a discrete vector-quantization bottleneck, collapsing duplicated residual-stream features into compact, interpretable concept vectors. Our approach combines top-k temperature-based sampling with exponential moving average (EMA) codebook updates, providing controlled exploration of the discrete latent space while maintaining codebook diversity. Across both encoder- and decoder-based models on ERASER-Movie, Jigsaw, and AGNews, CLVQ-VAE outperforms clustering, single-layer vector quantized-variational autoencoder (VQ-VAE), and sparse autoencoder (SAE) baselines across three evaluation axes: removing identified concepts drops downstream probe accuracy by up to 93%, LLM judges rank our concepts first in 66.7% of comparisons, and human annotators recover model predictions from our visualizations with 78% accuracy versus 54% for clustering.

Ankur Garg, Xuemin Yu, Hassan Sajjad +1

Variational Autoencoders LLM Interpretability Vector-Quantized Variational Autoencoder Sparse Autoencoders Language Model Probing

Jun 23, 2025

Latent Space Analysis for Interpretable Uncertainty in Melanoma Classification

Melanoma is a highly aggressive skin cancer, making early and accurate diagnosis critical. While deep learning excels in skin lesion classification, standard ``black-box" models struggle to explain diagnostic uncertainty, limiting clinical trust. This work introduces a hybrid framework combining a class-aware adversarial Variational Autoencoder and an XGBoost classifier, transcending simple binary classification by leveraging a generative latent space for interpretable decision support. Guided by adversarial training, the model learns the visual characteristics of skin lesions and projects them into a continuous latent space, ensuring that similar images are grouped closely together. Trained on this latent space, the XGBoost classifier achieves a robust AUC of 0.868, competing closely with state-of-the-art models. For borderline cases, the framework enables clinicians to leverage the latent topology through Content-Based Image Retrieval. This provides a dual benefit: it allows the clinician to visually compare an ambiguous lesion against biopsy-confirmed precedents and acts as an early warning sign since a borderline classification can indicate that a lesion shares features of both nevi and melanomas, potentially requiring close monitoring. Our approach translates algorithmic hesitation into transparent, evidence-based visual support, bridging the gap between predictive performance and clinical trust.

Ciro Listone, Aniello Murano

University of Naples Federico II, Naples, Italy.

Variational Autoencoders Skin Lesion Classification Uncertainty Quantification Medical Image Classification Explainable Medical Image Analysis Image Retrieval+1

Jun 20, 2025

Variational Learning of Disentangled Representations

Disentangled representations separate factors that are shared across conditions from those that are condition-specific. Such separation is needed for generalization to new domains, treatments, patients, or species. A dominant line of work pursues this goal through variational formulations. While these approaches achieve partial disentanglement, they often exhibit three common limitations: they either do not remove all condition-specific information from the condition-specific representation, allow the condition-specific representation to become uninformative, or impose independence assumptions that do not reflect the underlying generative process. In this work, we introduce DisCoVR, a variational framework that addresses these limitations. Its objective is aligned with the probabilistic structure of the data-generating process, and includes an adversarial term that prevents condition-specific information from being encoded in the condition-specific representation.DisCoVR reconstructs the data from both shared and condition-specific representations, ensuring that each remains informative, and uses a structured prior that further reinforces the informativeness of both representations. We show that across synthetic, image, and single-cell RNA-sequencing datasets, DisCoVR achieves stronger disentanglement compared to previous approaches.

Yuli Slavutsky, Ozgur Beker, David Blei +1

Department of Statistics, Columbia University, New York City, USA · Irving Institute for Cancer Dynamics, Columbia University, New York City, USA · Department of Computer Science, Columbia University, New York City, USA +1

Variational Autoencoders Disentangled Representation Learning Latent Variable Models

Jun 1, 2025

Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis

Despite the empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their generalization performance remains theoretically underexplored, especially lacking a full consideration of the shared encoder-generator structure. Leveraging recent information-theoretic tools, we propose a unified theoretical framework that provides guarantees for the generalization of both the encoder and generator by treating them as randomized mappings. This framework further enables (1) a refined analysis for VAEs, accounting for the generator's generalization, which was previously overlooked; (2) illustrating an explicit trade-off in generalization terms for DMs that depends on the diffusion time

T

; and (3) providing computable bounds for DMs based solely on the training data, allowing the selection of the optimal

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and the integration of such bounds into the optimization process to improve model performance. Empirical results on both synthetic and real datasets illustrate the validity of the proposed theory.

Qi Chen, Jierui Zhu, Florian Shkurti

Department of Computer Science, University of Toronto · Data Science Institute · Vector Institute +2

Variational Autoencoders Neural Network Generalization Information-Theoretic Generalization Bounds Diffusion Models Generalization Bounds

Aug 2, 2024

Autoencoders in Function Space

Autoencoders have found widespread application in both their original deterministic form and in their variational formulation (VAEs). In scientific applications and in image processing it is often of interest to consider data that are viewed as functions; while discretisation (of differential equations arising in the sciences) or pixellation (of images) renders problems finite dimensional in practice, conceiving first of algorithms that operate on functions, and only then discretising or pixellating, leads to better algorithms that smoothly operate between resolutions. In this paper function-space versions of the autoencoder (FAE) and variational autoencoder (FVAE) are introduced, analysed, and deployed. Well-definedness of the objective governing VAEs is a subtle issue, particularly in function space, limiting applicability. For the FVAE objective to be well defined requires compatibility of the data distribution with the chosen generative model; this can be achieved, for example, when the data arise from a stochastic differential equation, but is generally restrictive. The FAE objective, on the other hand, is well defined in many situations where FVAE fails to be. Pairing the FVAE and FAE objectives with neural operator architectures that can be evaluated on any mesh enables new applications of autoencoders to inpainting, superresolution, and generative modelling of scientific data.

Justin Bunker, Mark Girolami, Hefin Lambley +2

Department of Engineering University of Cambridge Cambridge, CB2 1TN, United Kingdom · Department of Engineering, University of Cambridge · and Alan Turing Institute +3

Variational Autoencoders Autoencoders Scientific ML

Apr 20, 2022

Unsupervised Domain Adaptation for Cardiac Segmentation: Towards Structure Mutual Information Maximization

Unsupervised domain adaptation approaches have recently succeeded in various medical image segmentation tasks. The reported works often tackle the domain shift problem by aligning the domain-invariant features and minimizing the domain-specific discrepancies. That strategy works well when the difference between a specific domain and between different domains is slight. However, the generalization ability of these models on diverse imaging modalities remains a significant challenge. This paper introduces UDA-VAE++, an unsupervised domain adaptation framework for cardiac segmentation. We show that the evidence lower bound of VAE-based domain adaptation penalizes the mutual information between the image and the latent space, including the structure information that segmentation relies on. Maximizing the structure mutual information removes this penalty on the structure information, while the remaining information is still compressed. To estimate this term, we develop a novel Structure Mutual Information Estimation (SMIE) block with a global estimator, a local estimator, and a prior information matching estimator to maximize the mutual information between the reconstruction and segmentation tasks. Specifically, we design a novel sequential reparameterization scheme that enables information flow and variance correction from the low-resolution latent space to the high-resolution latent space. Comprehensive experiments on benchmark cardiac segmentation datasets demonstrate that our model outperforms previous state-of-the-art qualitatively and quantitatively. The code is available at https://github.com/LOUEY233/Toward-Mutual-Information

Changjie Lu, Shen Zheng, Gaurav Gupta

College of Science and Technology, Wenzhou-Kean University, Wenzhou, China

Unsupervised Domain Adaptation Medical Image Segmentation Mutual Information Maximization Cross-Modality Medical Image Segmentation Variational Autoencoders