Generative Modeling

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39 papers in the last four weeks, up 144% on the four weeks before. 0.4% of all new papers.

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Latest papers 347

Aug 12, 2026q-fin.MF

DYSANOS Generative Dynamic Smooth Arbitrage-free Non-parametric Option Surfaces

This article presents with DYSANOS the first generative market model for smooth SANOS option surfaces for all strikes and expiries which are free of static arbitrage. Our model is designed to generate entire paths of daily spot and option prices for years in the future. We present a robust and useful if somewhat simplistic baseline in the form of an AR(1) model. We discuss model setup, data pipeline, and training and investigate market reconstruction, stability, and tail behavior. We illustrate model performance on 891 Option Metrics IvyDB S&P Index surfaces from 2022-01-03 through to 2025-08-29. We also demonstrate how to construct numerically a risk-neutral density. As part of this we develop a new test for zero conditional means under a given measure. We show that for 100,000 simulated paths a trading universe of 48 options and spot is numerically free of dynamic arbitrage.

Hans Buehler, Blanka Horvath, Anastasis Kratsios +1

Mathematical Institute and Oxford-Man Institute, University of Oxford. · McMaster University and Vector Institute.

Quantitative Finance Generative Modeling Financial Time Series

Aug 12, 2026cs.LG

Unifying Generative Models with Path Integrals

We formulate generative modeling as a path integral in which flow-based, diffusion-based, variational, and adversarial models arise as different evaluation principles for a single master action. Its Martin-Siggia-Rose-Janssen-de~Dominicis (MSRJD) form separates free from interacting probability flows and opens them to diagrammatic perturbation theory. The expansion yields a one-loop correction to deterministic samplers at no stochastic-sampling cost, which we validate on solvable and nonlinear drifts, where it reduces a 53 % tree-level error to 1.6 %. Imperfect learned scores enter as insertions and yield a response-weighted score-matching objective, and symmetry-equivariant drift design becomes an operator expansion with EFT power counting.

Ramon Winterhalder

TIFLab, Dipartimento di Fisica, Università degli Studi di Milano · and INFN, Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy

Generative Modeling Flow-Based Generative Modeling

Aug 12, 2026stat.ML

Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics. The method is the Wasserstein gradient flow of the Lipschitz-regularized Kullback-Leibler (KL) divergence penalized by a Conditional Value-at-Risk (CVaR) discrepancy term: the Lipschitz-regularized KL divergence enables robust learning under minimal assumptions on the target distribution, while the CVaR penalty restores the velocity that otherwise vanishes prematurely in the under-sampled tails. The penalized flow admits a bounded but non-Lipschitz velocity field. This departs from the Lipschitz transport maps of standard generators, which preserve the tail behavior of a light-tailed source, and enables transport toward heavier-tailed targets. To define this flow on empirical measures, we derive the first-variation subgradients of CVaR from its Rockafellar-Uryasev representation, valid precisely where the classical density-based formula fails. The particle algorithm CVaR-GPA fine-tunes the output samples of any pre-trained model, without access to its architecture, and runs on an adaptive time horizon set by a kinetic-energy stopping criterion rather than a preset depth. On synthetic isotropic and anisotropic Student-

t

target distributions, Neal's funnel distribution, and the real-world high-dimensional Fama-French 25 portfolio dataset, CVaR-GPA dramatically improves global and tail accuracy on heavy-tailed targets over the pre-trained baseline.

Thejani Gamage, Hyemin Gu, Zhizhen Zhang +3

Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA · School of Data and Information Sciences (SDIS) and Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC

Wasserstein Gradient Flows Generative Modeling Heavy-Tailed Distributions

Aug 11, 2026cs.LG

Generator-Guided Inverse Sampling for Lévy-Driven Generative Models

This paper studies inverse sampling for Lévy-driven generative models from the perspective of Markov generators. Unlike conventional diffusion models, Lévy-driven dynamics involve infinite jump activities, which makes their reverse process nonlocal and difficult to characterize using score information alone. We address this challenge by analyzing the forward and reversed generators. It is derived that the reversed jump component generally becomes a state-dependent Markov jump process governed by a nonlocal density ratio. This observation motivates a structured reverse sampler that decomposes the dynamics into diffusion, small jump, and large jump components. Based on this characterization, we develop a computationally tractable sampler for a class of isotropic linear Lévy SDEs with symmetric

α

-stable jump components. For the jump component, the neural network is used only to amortize the rate of large jump activities, while jump amplitudes are generated from analytically derived conditional distributions, which improves interpretability and controllability. Efficient implementation techniques are further introduced under this setting to avoid expensive high-dimensional integration and sampling. The sampler is further adapted to approximate observation-guided sampling and applied to OFDM-SISO channel estimation under mixed Gaussian and impulsive noise. Simulations show robust estimation performance with a favorable tradeoff between complexity and performance.

Tianfu Qi, Jun Wang, Jun Zhang

National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China, Chengdu 611731, China · Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, China

Posterior Sampling Generative Modeling

Aug 10, 2026cs.AI

Renormalising Generative Models for Active Inference: Foundations, Derivations, and Verification

Active inference offers a unified framework for perception, learning, and action, but scaling discrete active-inference models to rich spatial and temporal domains remains difficult. Renormalising generative models (RGMs) address this challenge by composing discrete generative models across spatial and temporal scales, coarse-graining lower-level states and paths into higher-level causes for objects, events, and action. However, fully reproducing and adapting the framework remains difficult: the mathematical exposition is compact, and the reference implementations are deeply integrated within specialized software environments, leaving many algorithmic details implicit. This paper addresses these challenges by providing a self-contained, derivation-oriented account of RGMs together with an open, verified implementation. We explain how the hierarchy is built, how beliefs and actions are updated within it, and how information is passed between levels. Where the published equations and implementation differ in emphasis, we make those choices explicit and explain their modelling consequences. By clarifying the theory and separating it from its original implementation context, this work lowers practical barriers to entry and makes RGMs more transparent, auditable, and reproducible, providing a foundation for future quantitative evaluation and development on machine-learning benchmarks.

Karim Zaghw, Andrew Pashea, Marc Pritsch +3

University of Tübingen, Tübingen, Germany · Division of the Social Sciences, University of Chicago, Chicago, IL, USA · Heidelberg University, Heidelberg, Germany +3

Active Inference Generative Modeling

Aug 10, 2026cs.LG

Imaginative Generative AI: Crossing the Entropy Wall into Worlds Beyond Imitation

Generative AI models are primarily designed to imitate the data distribution, an objective that neither corrects diversity lost by a learned generator nor defines how generation should extend beyond the diversity of the data itself. We introduce Imaginative Generative AI (IGA), a framework that makes diversity part of the target-distribution design problem: among distributions close to a reference, IGA selects one whose spectral diversity reaches a prescribed level. Diversity is measured by the von Neumann entropy of the generated distribution's kernel covariance operator in a fixed representation space, providing a reference-free representation-guided measure of how broadly probability mass occupies embedding directions. The spectral entropy of the population data distribution defines an Entropy Wall. Below the wall, IGA performs diversity repair, recovering variation that a learned generator has lost while remaining within the diversity level of the data. Beyond the wall, the data distribution itself becomes infeasible, and IGA deliberately departs from it to produce distributions with greater representation-relative spectral diversity, an operational notion of imaginative generation. These regimes form a single regularization path from imitation to imagination and define an i.i.d. target distribution at each prescribed diversity level. We develop the theory of this entropy-constrained projection and show that, under a KL anchor to a pretrained generator, the optimum satisfies a self-consistent exponential-tilt relation. This characterization leads to IGA Guidance, a retraining-free inference-time method for score-based and diffusion models, including DDPM and DDIM samplers. Experiments on synthetic and vision benchmarks demonstrate diversity repair below the Entropy Wall and controlled spectral extrapolation beyond it.

Farzan Farnia, Hossein Goli, Amin Gohari

Department of Computer Science and Engineering, The Chinese University of Hong Kong · Department of Information Engineering, The Chinese University of Hong Kong

Constrained Generative Modeling Diffusion Model Guidance Generative Modeling

Aug 10, 2026cs.CV

ControlRadio: Prompt-Driven Controllable Diffusion for Cross-Modal Radio Map Generation

Radio maps describe how wireless signals propagate across space and are essential for wireless communication, sensing, and network planning. However, constructing accurate radio maps traditionally requires either dense measurements or computationally expensive physical simulations, which limits scalability and real-time deployment. Recent advances in generative artificial intelligence offer a promising alternative, but existing approaches lack fine-grained control and physical consistency when applied to real-world wireless environments. Here we present \textbf{ControlRadio}, a controllable generative framework that produces radio maps from natural-language descriptions and environmental layouts, including building structures and transmitter locations. Joint semantic and spatial conditioning enables interpretable, propagation-plausible generation, while a controlled latent prior and layout-aware conditioning improve stability and structural consistency. Extensive experiments demonstrate that ControlRadio achieves state-of-the-art accuracy and strong generalization across diverse urban scenarios, while reducing computation time by more than four orders of magnitude compared with conventional simulation-based methods. Such results suggest a new paradigm for scalable and controllable wireless environment modeling, with broad implications for next-generation communication systems and data-driven radio sensing.

Kangjun Liu, Xiying Pan, Shuhang Zhang +3

Pengcheng Laboratory, China · South China University of Technology and the Pengcheng Laboratory, China · Peking University, China +2

Wireless Communications Generative Modeling Radio Propagation Modeling Conditional Generative Modeling Diffusion Models

Aug 8, 2026cs.AI

Generative Models: Principles, Architectures, and Applications

Generative AI has emerged as one of the most transformative forces in modern artificial intelligence, reshaping how we create, imagine, and interact with digital content. From photorealistic images to coherent text, from immersive videos to novel molecular structures, generative models now power applications that were once confined to science fiction. This book is designed to guide readers through the foundational principles, mathematical underpinnings, and practical architectures that underpin this revolution.

Jun Lu

Image Generation Generative Modeling Text Generation

Aug 7, 2026stat.ML

Leveraging generative models to assist Monte Carlo sampling

Sampling high-dimensional probability distributions is a central task in scientific computing, with applications ranging from Bayesian inference to statistical physics and molecular simulation. Despite decades of methodological developments, two major challenges remain: scaling to high dimensions and efficiently exploring multimodal distributions characterized by metastable states. Classical approaches such as Markov chain Monte Carlo, tempering methods, or enhanced sampling based on collective variables have achieved major successes, but they also face intrinsic limitations. This tutorial review explores a new paradigm that has recently emerged at the interface of machine learning and computational statistical physics: the use of generative models as tools for sampling. In this context, models such as normalizing flows and diffusion models are not used in their traditional data-driven setting, but rather as flexible probabilistic models that can assist the sampling of distributions known only up to a normalization constant. This manuscript reviews the early development of this rapidly evolving field and discusses several methodological directions, including exact samplers based on generative models and strategies to train such models in the absence of data. While an exhaustive survey of the literature is not attempted, we present a selection of key ideas and methods, along with a discussion of their strengths and limitations. The review is intended to be an accessible tutorial for both physics and machine learning audiences, and it aims to provide a starting point for researchers interested in exploring this exciting area of research.

Marylou Gabrié

Laboratoire de Physique Statistique, École normale supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France

Normalizing Flows Generative Modeling Diffusion Models

Aug 7, 2026cs.LG

Fluid-DiT: Graph-Free Diffusion Transformers for Fluid Flow Simulations Learning

Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive. Recent advances, such as Diffusion Graph Networks (DGNs), have combined diffusion models with graph neural networks to sample equilibrium states directly from unstructured meshes, enabling distributional accuracy even from short simulations. However, graph-based diffusion approaches suffer from hand-crafted architectural constraints, limited receptive fields in message passing, and costly multi-scale designs, which restrict scalability to larger and more complex domains. We propose Fluid-DiT, a Graph-Free Diffusion Transformer that replaces graph message passing with attention-based denoising, eliminating explicit graph design while preserving the ability to model distributions of chaotic flows. Our framework introduces a latent-space formulation that disentangles geometric fidelity from distributional learning, reducing high-frequency artifacts and accelerating sampling. By leveraging the transformer's global receptive field, Fluid-DiT naturally captures both local flow structures and long-range correlations without requiring hierarchical graph coarsening. On canonical benchmarks including laminar cylinder wakes, ellipse-flow systems, and turbulent 3D wing experiments, Fluid-DiT consistently outperforms graph-based diffusion baselines in both sample quality and distributional accuracy, achieving higher

R^2

correlations and lower Wasserstein distances. Moreover, it generalizes robustly from short, incomplete trajectories to unseen Reynolds numbers and geometries, demonstrating strong scalability.

Shentong Mo, Guolin Ke

CMU · DP Tech

Diffusion Transformer Generative Modeling Diffusion Models Computational Fluid Dynamics

Aug 5, 2026cs.LG

Why the Third Axis Is Freedom

In generative training, a model produces an output and is penalised for its difference from an example. With one output per comparison, a model that produces one common answer can outperform a model retaining a broader repertoire. Explorative Modeling (XM) produces

K

outputs per comparison and updates on the closest, claiming exploration as a "third pretraining axis" associated with generative expressivity. Here I show the third axis is actually freedom, meaning the weakness of the constraint implied by a model's behaviour. Previous work showed freedom is a property of function rather than form. Parameters, architecture, minimum-description-length (MDL), and data can vary while the behavioural constraint remains unchanged. It was formally proved that weakest models are likeliest to generalise, and freedom selection beat MDL by 110-500% in induction experiments. I prove average XM loss depends on the chance a candidate misses an acceptable region, with exploration raising miss probability to power

K

. For

K>1

, match probability rises with freedom. I then demonstrate empirically that XM optimises for freedom. In a Forward XM experiment, larger

K

increased or saturated measured freedom, and increased freedom at every tested value under context-dependent targets. I trained XM candidate pools and compared validation selection with a freedom selector that read unlabelled parent contexts. Freedom won in 29 of 30 cases. Generative expressivity is a mode-count proxy for freedom, that discards the extension structure that gives freedom its generalisation significance. XM is a means, freedom an end, and selecting for freedom improved XM under distribution shift.

Michael Timothy Bennett

Machine Intelligence and Normative Theory Lab, The Australian National University Canberra, ACT 2601, Australia

OOD Generalization Generative Modeling

Aug 5, 2026quant-ph

Representational separation between unitary and channel quantum generative models via shared classical randomness at shallow depth

Near-term quantum hardware limits circuit depth and often imposes geometrically local connectivity for quantum generative models, restricting the output distributions accessible to shallow unitary Born models. Introducing stochasticity into a unitary quantum Born model can improve the empirical generative performance of the resulting channel model and, for a restricted small-scale architecture, has been proven to represent a strictly larger family of distributions than its unitary counterpart. However, whether such randomness provides a provable separation at fixed shallow depth for arbitrarily large systems has remained open. Here, we show that shared classical randomness, a comparatively weak resource from entanglement theory, is sufficient to establish such a strict scalable representational separation over the corresponding shallow unitary Born model. More specifically, we augment bounded-connectivity shallow unitary circuits, followed by computational-basis measurements, with spatially separated local Pauli operations, whose joint application is controlled by a single classically sampled random bit. The resulting shallow-depth channel model generates long-range correlations in the classical output distribution that no purely unitary shallow-depth model with bounded connectivity can reproduce. For one-dimensional nearest-neighbour architectures, reproducing such distributions with a purely unitary model can require depth

Ω(N)

in the worst case. We further show that measurement-based quantum computation (MBQC) provides a natural implementation of the required shared classical randomness through suitable adaptation of the random measurement outcomes. Numerical experiments on MBQC-based generative models support the analytical results.

Arunava Majumder, Marius Krumm, Hendrik Poulsen Nautrup +1

University of Innsbruck, Department of Theoretical Physics, Technikerstraße 21a, A-6020 Innsbruck, Austria.

Quantum Generative Modeling Quantum Machine Learning Generative Modeling

Aug 5, 2026cs.LG

Marginal Matching Does Not License Factorized Sampling: Auditing Conditional Style Leakage in Factorized Generative Models

Factorized generative models commonly regularize a latent style variable z_s by matching its marginal distribution to a fixed Gaussian prior and interpret this as evidence that the style representation is independent of class information. We show that this interpretation is incorrect. Matching only the marginal distribution places no constraint on the class-conditional distributions, allowing the latent style to remain highly predictive of the label despite appearing perfectly Gaussian in aggregate. We derive an exact decomposition showing that this mismatch is one of four conditions required for factorized sampling, and demonstrate that eliminating it is necessary but not sufficient to obtain the intended factorization. Empirically, our case-study model and four representative latent baselines achieve near-zero global MMD while still allowing a linear probe to recover class labels with 74%--100% accuracy (10% chance level). Our model reaches 99.15% clustering accuracy, whereas externally evaluated class-conditional generation succeeds only 16% of the time. This leakage remains under six independent perturbations involving model capacity, curriculum, prior geometry, and supervision across two datasets. Four mitigation strategies reduce probe accuracy to 21%--46%, although they leave within-class dependence largely unchanged. A post-hoc conditional prior improves externally evaluated class generation to 0.97 on MNIST without retraining but reaches only 0.41 on CIFAR-10, while an empirical style bank achieves 0.88 on CIFAR-10. These results demonstrate that no divergence computed solely on the marginal distribution of the style latent can certify independence from class labels, and that reporting marginal statistics alone does not verify the property commonly claimed in factorized generative models.

Duong Bach, Hai Nguyen Hong, Cuong Do

Smart Health Center (VISHC), VinUniversity, Ha Noi, Viet Nam

Disentangled Representation Learning Latent Variable Models Generative Modeling Conditional Generative Modeling

Aug 5, 2026stat.ML

Intrinsic-Hybrid Latent Diffusion Models for Generative Modeling on Unknown Manifolds

We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure. Latent diffusion models (LDMs) address the high dimensionality by learning a latent space, but they typically impose a Euclidean structure, failing to capture the underlying manifold geometry, especially problematic in data-sparse regimes. ILDM addresses these limitations by interpreting the latent space as a chart of an unknown Riemannian manifold, with geometry and uncertainty quantified through a probabilistic decoder. The forward process is a hybrid diffusion that switches between Riemannian and Euclidean dynamics based on local uncertainty, where the Riemannian component is governed by a probabilistic metric tensor derived from the decoder. To learn the generative dynamics, we introduce an approximate denoising score matching method tailored to the hybrid diffusion setting, enabling a backward process defined by hybrid Langevin dynamics. Experiments on COIL-100, MNIST, and cardiac MRI datasets demonstrate that ILDM significantly improves generation quality, achieving lower FID and LPIPS scores compared to standard diffusion and latent diffusion models.

Yizhu Wang, Mu Niu, Xiaochen Yang

School of Mathematics and Statistics, University of Glasgow, Glasgow, U.K.

Latent Diffusion Models Generative Modeling Diffusion-Based Image Generation Score-Based Generative Modeling Diffusion Models

Aug 3, 2026cs.LG

Federated generative event models for tokenized electronic health records

Electronic health record foundation models are limited by institutionally siloed data and substantial performance degradation under cross-site transfer. We evaluated federated training of tokenized generative event models (GEMs) across 122,251 intensive care hospitalizations from three independent health systems harmonized to the Common Longitudinal ICU Data Format. Models were assessed on 12 post-24-hour clinical prediction tasks using within-site, cross-site, centralized, and federated training configurations. GEMs achieved the highest mean within-site and cross-site ROC-AUC and were substantially more transportable than conventional supervised models: their average cross-site penalties were 0.025 ROC-AUC and 0.027 PR-AUC, compared with 0.079 and 0.089 for LightGBM. Federated Learning (FedAvg and FedAvgM) approached the performance of centralized GEM training, with most gains obtained within 5-10 communication rounds. However, centralized multi-site training provided only modest improvements over complete local training. Multi-site models were most useful when local training data were limited, with their advantage narrowing as institutional data accumulated. These findings show that federated GEM training is technically feasible and preserves most centralized performance, but that the main open challenge is learning transportable representations to translate larger, but heterogeneous data from multiple health systems into a reliable target-site benefit.

Michael C. Burkhart, Luke Solo, Inhyeok Lee +8

Department of Medicine, University of Chicago, Chicago, Illinois, USA · Department of Medicine, Northwestern University Feinberg School of Medicine, Chicago, Illinois, USA

Clinical Outcome Prediction Generative Modeling Longitudinal EHR Modeling Cross-Dataset Generalization Federated Learning

Aug 2, 2026cs.CV

SPAE: Spectrally Guided Autoencoder for Pretrained Visual Latents

Latents from vision foundation models (VFMs) are semantically rich and well suited for visual understanding. Recent representation autoencoder methods such as RAE have shown that they can provide promising latent spaces for image generation. However, VFM latents remain difficult to model directly: DiT-generated latents exhibit spectral mismatch with encoder latents, especially in high-frequency components. Our channel-wise spectral analysis further reveals that these high-frequency components are diffusely distributed across latent channels and entangled with semantic information, making the latent space difficult for DiT to model. To address these challenges, we propose SPAE, latent adaptation framework for generation. Specifically, SPAE employs a compact bottleneck to distill stable semantic information while suppressing high-frequency components, thereby improving the alignment between DiT-generated latents and encoder latents. In addition, we apply a channel-wise masking strategy to promote the decoupling of semantic information and high-frequency details across bottleneck channels. Experiments show that SPAE achieves a favorable balance among visual understanding, generation quality, and reconstruction fidelity.

Yibin Huang, Jixiang Hong, Zongzhao Li +8

Alibaba Group · Gaoling School of Artificial Intelligence, Renmin University of China

Autoencoders Vision Foundation Model Adaptation Generative Modeling Diffusion-Based Image Generation

Aug 2, 2026cs.LG

One-Sided Quantile Coupling for Flow Matching

Flow Matching trains continuous-time generative models by regressing the velocity field of a probability path between a simple source distribution and a target data distribution. The coupling that pairs source and target samples strongly affects optimization and sample quality, but structured couplings typically rely on mini-batch transport or assignment procedures whose cost grows at least quadratically in batch size. We propose Quantile Coupling Flow Matching (QC-FM), a lightweight one-sided coupling: rather than matching two pre-sampled batches, it samples only the data batch and constructs each paired source directly. Data ranks projected along a small number of random orthogonal directions are mapped to Gaussian quantiles, and the latent code is completed in the orthogonal complement by conditional Gaussian sampling. The construction is one-dimensional per slice, so the coupling requires no pairwise cost matrix and no assignment to solve. We show that, for each drawn frame, this coupling eliminates the irreducible regression variance along every selected slice and makes the ideal flow exactly straight there, while leaving the sampling prior unchanged: generation still starts from the standard Gaussian, and the training source deviates from it only through the copula of the slice codes, whose transport cost we bound. For training, we apply QC to an anchor subset and complete the remaining source slots with exact Gaussian samples, retaining the QC bias while preserving an explicit signal from the Baseline coupling. Across CIFAR-10, CelebA, FFHQ, and ImageNet-64, QC-FM improves over the Baseline under matched training budgets, reducing FID by up to 12.9%, and outperforms OT-CFM on all four datasets. These results suggest that preserving projected rank structure is a simple and scalable way to inject useful geometric bias into FM couplings without solving a mini-batch transport problem.

Jin-Young Kim, So-Yoon Cho, Hyun-Gyoon Kim

Independent Researcher · Division of Finance & AI, Hankuk University of Foreign Studies · Dept. of Financial Engineering, Ajou University

Flow Matching Image Generation Distribution Matching Generative Modeling Flow-Based Generative Modeling

Aug 1, 2026cs.CV

Beyond Token-Level Cross-Entropy: Fréchet Distributional Post-Training for Autoregressive Image Generation

Autoregressive image generators are commonly pretrained with token-level cross-entropy under teacher forcing, yet evaluated by the distributional quality of decoded images. This creates an objective mismatch, because categorical errors have unequal image-level consequences, and a context mismatch, because inference conditions on model-generated histories. We introduce FD-loss post-training, which adapts a pretrained discrete generator using representation-space Fréchet distance as the sole objective. A dual-pass scheme first constructs detached rollout contexts through gradient-free generation under the model's native inference configuration, then performs differentiable replay with a probability-level straight-through estimator (STE) that preserves hard argmax decoding in the forward pass while propagating image-level gradients through temperature-scaled probabilities. Only the generator is updated, while the tokenizer and feature extractors remain frozen. Across eight completed configurations from four generator families on class-conditional ImageNet at

256\times256

, FD-loss post-training reduces FID and

\mathrm{FD}_{r6}

by 41.4% and 52.0% on average. The strongest FID result improves from 2.42 to 1.43 without adding parameters or inference steps.

Jinhua Zhang, Yisong Lin, Wei Long +1

University of Electronic Science and Technology of China

Generative Modeling Autoregressive Image Generation

Jul 30, 2026cs.AI

MUL-T: Decoding Spatial Cellular Architecture in Multiplexed Tissue Images

Understanding tissue organisation in multiplexed imaging requires modelling both cellular phenotypes and their spatial context. Existing approaches typically rely on handcrafted features, such as marker intensity statistics or cell-type proportions, which often fail to scale or generalise across cohorts with heterogeneous marker panels. We introduce MUL-T, a lightweight transformer framework that reframes tissue architecture as a masked contextual prediction task over discrete cell tokens. By learning contextualised [CLS] embeddings without task-specific supervision, the model captures higher-order cellular interactions while remaining computationally efficient. We evaluate MUL-T on several clinically relevant downstream tasks, including core-level tumour pattern classification, patient-level grading, PD-L1 positivity prediction, and cross-dataset treatment response prediction. Across tasks, MUL-T consistently outperforms classical feature-based baselines and achieves performance comparable to a foundation ViT model, despite substantially fewer parameters and lower training cost.

Farzaneh Seyedshahi, Kai Rakovic, Adalberto Claudio Quiros +2

Cancer Research UK Scotland Institute, Glasgow, UK · University of Glasgow, Glasgow, UK

Transformer Generative Modeling Histopathology Image Classification Medical Image Representation Learning Microscopy Image Analysis

Jul 29, 2026cs.LG

SE(3)-MeanFlow: Few-Step Protein Backbone Generation on Lie Groups

Generative modeling of protein backbones promises the de novo design of proteins with prescribed structural and functional properties. Existing diffusion and flow-matching models produce high-quality backbones on SE(3)^N, but inference requires numerically integrating an ODE over hundreds of network evaluations, each involving a Lie group exponential map - a bottleneck for high-throughput design campaigns. We introduce SE(3)-MeanFlow, a few-step generative framework that extends MeanFlow from Euclidean space to the Lie group geometry of protein frames. Working natively in the Lie algebra so(3) and in R^3, we derive closed-form average-velocity identities for rotations and translations, giving simulation-free training targets. We further introduce an SE(3) alpha-Flow objective that removes the Jacobian-vector product from the rotation branch and serves as a warm-up stage, after which training switches to a small-t stabilized MeanFlow loss that is used for the remainder of pretraining and for rectification-based post-training. In protein backbone generation, SE(3)-MeanFlow matches or exceeds flow-matching baselines that use several times more sampling steps, and its advantage widens in the few-step regime, where rectification lets it lead at every matched budget - at a modest cost in diversity.

Yikun Bai, Binghang Lu, Yikai Liu +7

Department of Mathematics, Purdue University · School of Electrical and Computer Engineering, Purdue University · Department of Biochemistry, Purdue University +5

Flow Matching Lie Group Methods Generative Modeling 3D Molecular Generation Mean Flow Molecular Generation+2

Jul 29, 2026cs.LG

Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generation

The deep learning revolution, kicked off by AlexNet, taught us that end-to-end training beats decomposing a problem into hand-designed stages. Generative modeling, however, has remained the exception-despite generative models being remarkably capable, they are still not trained end-to-end. This is because, at its core, generative modeling is about handling distributions with many modes, and existing scalable approaches handle this the same way, by factoring the generation procedure, which prevents end-to-end generation. In this work, we introduce Explorative Modeling, a new paradigm that instead factors the training loop, exploring K candidate matches between model generations and data, and training on the best, so predictions commit to modes rather than blurring them. We find Explorative Models (XMs) useful in two settings. First, increasing exploration adds a third pretraining axis beyond parameters and data for existing generative models-where scaling exploration monotonically improves performance across both continuous and discrete domains (images, video, and language). Notably, gains from exploration increase with scale, climbing from 7% to 36% as data scales and from 13% to 23% as models grow, with efficiency gains more than doubling at 3x the compute. Concretely, exploration improves FLOP efficiency by 4.1x, sample efficiency by 6.2x, parameter efficiency by 47%, lifts the strongest of image-generation recipes to a near-state-of-the-art 1.43 FID on ImageNet without guidance, enables scaling how end-to-end existing models are, and unlocks scaling generalization. Second, XMs enable end-to-end reconstructive generative modeling, matching diffusion on control tasks with 16-256x fewer inference steps. Together, these results establish XMs as both a new pretraining axis for existing generative models and a standalone end-to-end generative modeling paradigm.

Alexi Gladstone, Heng Ji, Yilun Du

1UIUC · 2Harvard

Image Generation Generative Modeling AI Scaling Laws

Jul 29, 2026cs.CV

DistillAlign: Coordinating Mode Covering and Mode Seeking in Autoregressive Video Distillation

Existing autoregressive video distillation methods commonly adopt a Distribution Matching Distillation (DMD)-based multi-stage pipeline. However, they typically decouple the initialization and DMD stages -- which then pursue different target distributions -- and judge the intermediate student mainly by visual scores such as VBench. In this paper, we revisit this design from a distributional perspective. Given the mode-seeking nature of the distribution matching loss, a good initialization should match the mode coverage of the target DMD teacher, rather than merely pursuing high quality. To analyze this, we introduce a distributional evaluation protocol that measures precision and coverage between student and teacher distributions in a shared latent space. It exposes differences hidden by visual scores: some initializations reach high precision but low coverage, leading to suboptimal refinement, while mode-covering ones preserve broader support. Furthermore, even when the target distributions are aligned, DMD's reverse-KL objective can still drive the student toward high-probability teacher regions in late training, reducing coverage and diversity. To address this, we propose joint distillation, which combines DMD's mode-seeking objective with a Consistency Distillation-based mode-covering constraint. Experiments show that our method improves generation quality, coverage, and diversity; notably, even with a Wan-1.3B DMD teacher, it outperforms baselines refined with Wan-14B, underscoring the importance of distributional alignment in autoregressive video distillation.

Jiaxing Li, Kai Zou, Cindy Zhou +7

Riemann Dynamics · Nanyang Technological University · 1Riemann Dynamics, 2Nanyang Technological University +2

Generative Modeling Autoregressive Video Generation Distribution Matching Distillation

Jul 29, 2026cs.LG

Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality

We study generative modeling of spatial point processes (SPP), where both the number of points and their spatial configuration are governed by a joint distribution. While diffusion models have achieved strong performance in modeling complex distributions, extending them to variable-cardinality SPP remains challenging. Existing approaches either decouple the modeling of cardinality and spatial structure, or rely on discrete trans-dimensional operations to modify the number of points, resulting in inflexible and asymmetric generative dynamics. We propose the existence-field diffusion model (EFDM) for spatial point processes modeling, where each potential point is associated with an existence variable representing its degree of presence. This enables a unified diffusion process that jointly models both spatial locations and cardinality without requiring explicit discrete transitions. We demonstrate that our approach provides a flexible and general framework for generative modeling of spatial point processes, achieving improved modeling capability on datasets with varying cardinality.

Xiaoyin Pan, Christian R. Shelton, Rakshith Mahishi +1

University of California, Riverside · New York University · Zhongguancun Academy

Generative Modeling Diffusion Models

Jul 28, 2026cs.CV

Noise-Robust Conditional Flow Matching: Generating Clean Samples from Noisy Datasets

Generative models learn the statistical properties of their training data, so high-quality generation depends on clean and representative datasets. In scientific imaging, acquisition often yields noisy measurements, while collecting clean references can be costly, impractical or even unattainable. Training directly on these measurements results in a model that reproduces the corrupted data. This can be circumvented by learning the clean population distribution directly from the noisy data. Conditional flow matching (CFM) combines a simple regression objective with stable training, efficient sampling, and strong image-generation performance, making it a natural framework for this setting. We introduce Noise-Robust Conditional Flow Matching (NR-CFM), an unconditional generator that learns from one corrupted observation per image. NR-CFM provides a closed-form clean endpoint correction for additive white Gaussian noise and learns a data-driven correction for general Gaussian corruptions with more complex covariance structure. Across the evaluated corruption settings, NR-CFM outperforms NR-GAN in most cases and remains competitive with Ambient Diffusion in the high-noise regime. We further evaluate NR-CFM on scientific data at signal-to-noise ratios as low as

0.001

, where it generates plausible particle images from severely corrupted measurements.

Adrian Urbański, Gabriel della Maggiora, Artur Yakimovich

Center for Advanced Systems Understanding (CASUS), Görlitz, Germany · Helmholtz-Zentrum Dresden-Rossendorf e. V. (HZDR), Dresden, Germany · Institute of Computer Science, University of Wrocław, Wrocław, Poland +2

Flow Matching Image Generation Generative Modeling Flow-Based Generative Modeling

Jul 28, 2026stat.ML

Can Deep Generative Models Reproduce Non-Stationary Gaussian Random Fields?

Deep generative models (DGMs) are widely used for complex high-dimensional data and increasingly applied to spatial and spatio-temporal modeling. Their generated samples implicitly represent the learned data distribution and associated uncertainty. However, for real-world data, assessing whether DGMs have learned the underlying process is difficult because the ground truth is unknown and evaluation often relies on observations alone. We evaluate representative DGMs, flow matching (FM), DDPM, score-SDE, and VAE, on a known non-stationary Gaussian random field. This paper provides comprehensive metrics to assess recovery of the ground-truth mean and covariance structures, with oracle samples and a stationary control as references. All four models recover the mean surface, while their covariance recovery differs across model families: DDPM and score-SDE recover the covariance structure reasonably well, FM exhibits mildly attenuated non-stationarity and slight variance under-dispersion, and VAE has difficulty recovering the covariance structure. An experiment on ERA5 temperature anomalies further demonstrates how the framework can support the validation and development of DGMs for complex real-world spatio-temporal data.

Daniel Kua, Yan Song

Department of Statistics, University of British Columbia

Variational Autoencoders Flow Matching Generative Modeling Diffusion Models

Jul 27, 2026cs.LG

When Can You Correct Distribution Drift in Temporal Graph Generation? A Sharpening--Drift Tension and an Impossibility for Observation-Based Correction

Generative models of temporal graphs are trained on one stretch of an evolving network and deployed on the next, and they degrade badly in the gap. We show this degradation is derivable, general, and not fixable from observations. The masked flow-matching loss decomposes exactly, with no independence assumption, into an irreducible entropy plus a divergence whose derivative along the training path is positive precisely for structures rare during training and common at deployment, diverging as their training probability goes to zero. Empirically the trade-off is a power law with exponent

-0.605

(

R^2=0.9977

), and drift raises the sampler's error floor without changing how many steps reach it: across seven well-powered conditions the drift-period marginal error varies by at most

6\%

over a

50\times

range of sampling budgets, while the floor sits

2.2\times

to

34.3\times

above the in-period floor. Because the deployment period is observed, correction looks like a matter of measurement. It is not. We prove that any corrector measurable with respect to past observations leaves at least the conditional variance of the statistic it tracks, and that trend extrapolation beats trusting the last observation only when

μ^2>v(1-2ρ)

. Both premises are measurable and both go the wrong way: the drift is trendless and mean-reverting, with a one-step innovation as large as the drift itself. An oracle removes

60\%

of the error, the best observation-based corrector recovers

5.7\%

of that, and extrapolation is strictly worse than doing nothing clever.

Tianpeng Li, Xuan Guo, Wenjun Wang +2

College of New Media and Communication, Tianjin University · School of Artificial Intelligence, Tianjin University · School of Cyberspace Security,Hangzhou Dianzi University

Flow Matching Distribution Shift Graph Generation Generative Modeling Flow-Based Generative Modeling Drifting Models+1

Jul 27, 2026cs.CV

MSVS-VAE: Multi-Scale Anchored VecSet for High-Fidelity 3D Reconstruction

High-fidelity 3D generative modeling increasingly relies on the latent diffusion paradigm, where the reconstruction quality of the underlying 3D VAE becomes a primary bottleneck. Existing approaches largely follow two paradigms: sparse voxel-based representations achieve strong reconstruction quality but incur significant memory and computational overhead, while set-based representations are compact and continuous yet typically lag in fidelity due to latent sparsity and excessive global smoothness. We propose MSVS-VAE, a hierarchical set-based VAE that closes this fidelity gap without sacrificing compactness. Our key idea is to progressively densify anchored VecSet latents via hierarchical point-shuffle upsampling, increasing spatial capacity for fine-grained geometry modeling. To efficiently decode from the densified hierarchy, we replace global cross-attention with AVS-Conv, a geometry-aware local aggregation operator operating within local neighborhoods rather than the exhaustive latent set. We further introduce multi-scale query decoding to fuse coarse-to-fine latent features, where coarse scales provide stable global context, and fine scales refine localized geometry, reducing artifacts from overly local receptive fields. Extensive experiments on Objaverse, ABO, and in-the-wild benchmarks demonstrate that MSVS-VAE consistently outperforms prior set-based and voxel-based VAEs, delivering approximately 10x faster decoding than prior set-based methods and approximately 10x higher compactness than voxel-based baselines.

Dehao Hao, Kaiyi Zhang, Tanghui Jia +10

The Hong Kong University of Science and Technology, Hong Kong SAR, China · Peking University, Beijing, China · The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China +1

Variational Autoencoders 3D Reconstruction Generative Modeling 3D Representation Learning

Jul 27, 2026cs.LG

Physics-Guided Generative AI for Property-Targeted 3D Porous Media Design

Inverse design of three-dimensional porous media is central to applications in filtration, catalysis, energy storage, fuel cells, thermal management, and biomedical scaffolds, but remains challenging because many distinct pore geometries can share similar porosity or permeability while small structural changes can strongly affect transport behaviour. This paper proposes a physics-guided generative AI framework for property-targeted porous media design, combining a property-aware variational autoencoder, a conditional latent diffusion model, and an independently trained differentiable structure-to-property surrogate. The framework learns a compact, physically informative latent design space, generates porous structures conditioned on target porosity and directional permeability, and refines generated samples using property-level feedback during denoising and decoding. Experiments on procedurally generated structures and real micro-CT porous-media datasets show improved target-property matching, directional permeability control, and property correlation compared with representative property-aware variational-autoencoder and latent-diffusion baselines. The results demonstrate a scalable route towards controllable inverse design of complex porous geometries and establish a foundation for simulation-informed generative AI tools in engineering and advanced materials discovery.

Peng Wang

Centre for Vision, Speech and Signal Processing (CVSSP), University of Surrey, Guildford, UK

Generative Modeling Conditional Generative Modeling 3D Diffusion Models Inverse Design

Jul 26, 2026cs.AI

Offline-to-Online Creative Optimization with Generative Models and Adaptive Testing

Ad creative optimization is increasingly constrained by evaluation rather than generation. Generative models can produce many plausible creatives, but reliable evaluation requires online experiments, in which only a limited slate can be tested. We study how to use data from historical A/B tests to generate and select the candidates in that slate. We developed and deployed a performance-driven offline-to-online workflow that guides creative generation with a predictive model as an inference-time critic. In the offline phase, we use a predictive model trained on historical experiments to rank and refine variants created by a generative model. A final test slate is then deployed in an online adaptive experiment. In a 50-arm field experiment, we found that the best creative generated with this method yielded 45.1% higher engagement than the best human-authored creative. Two additional experiments showed the same upper-tail pattern, with lifts of 46.7% and 36.2%. We found that despite the predictive model being too noisy to directly identify the best creative offline, it effectively guides the generative model toward creating strong candidates that can be efficiently evaluated in an adaptive experiment. The results suggest a design principle for creative optimization with generative models: use predictive models to guide generation of a slate to test, judge the slate by whether it contains high-performing candidates at a feasible test size, and use adaptive experiments to select among candidates while limiting traffic lost to weak arms.

Kevin Lee, Benjamin Letham, Zhiyuan Jerry Lin +5

University of Michigan · USA · Meta

Online Advertising Generative Modeling A/b Testing

Jul 25, 2026cs.LG

Exploration of the generative capabilities of Boltzmann machines applied to social systems under the majority rule

We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions. To this end, we train deep belief networks (DBNs) with different configurations, where the first layer can use Gaussian visible units with more than two states (i.e., non-binary units). We then allow the DBN to "dream" samples conditioned on visible units that we keep fixed, and we measure the deviation of this dreamed system from the real one. We also corroborate, using a discrete thermometer based on a convolutional network, that the reconstructions remain in a critical state. Across several training sessions with different architectures, we show that, despite the complexity of the problem, the DBN can recover samples that remain critical even under input noise, with a gradual degradation of physical observables relative to the original sample.

Mauricio A. Valle, Gonzalo A. Ruz

Faculty of Engineering and Sciences Universidad Adolfo Ibáñez Millennium Nucleus for Social Data Science (SODAS) Santiago, Chile · Faculty of Engineering and Sciences Universidad Adolfo Ibáñez Millennium Nucleus for Social Data Science (SODAS) Millennium Nucleus in Data Science for Plant Resilience (PhytoLearning) Santiago, Chile

Generative Modeling Restricted Boltzmann Machines