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

Jul 25, 2026stat.ML

Logit-Coordinate Generative Models for Mixed Continuous-Categorical Tabular Data

Mixed continuous--categorical data pose a representation problem for continuous generative models. Flow Matching and Gaussian diffusion operate in Euclidean spaces, whereas categorical laws lie on probability simplices and may be highly imbalanced. We study a logit-coordinate framework that encodes categorical variables as smoothed natural parameters and combines them with transformed numerical variables. This yields common formulations of Logit Flow Matching and Logit Diffusion. We introduce a mixed-distribution discrepancy separating categorical marginal error from conditional continuous Wasserstein error, and derive stability bounds and imbalance-aware nonparametric rates linking vector-field or drift error to decoded mixed-distribution error. Controlled simulations show that scaled-logit coordinates improve or match one-hot coordinates, especially under severe rare-cell imbalance. Across four real-data benchmarks and ten splits per dataset, Logit FM improves the primary distributional metrics on three datasets and is comparable on Churn2; Block-Conditional Logit FM consistently improves the flat model; and Logit Diffusion generally improves over or matches One-Hot Diffusion.

Yuefei Shen, Xiaotong Shen

School of Statistics, University of Minnesota

Flow Matching Synthetic Tabular Data Generation Generative Modeling Diffusion Models

Jul 25, 2026cs.LG

All in One: Generative Modeling as Mean-Field Game Design

Mean-field games (MFGs) offer a unifying lens on continuous-time generative modeling: a cost tuple recovering twelve prominent models---Continuous Normalizing Flows, OT-Flow, Score-based Models, Schrödinger Bridges, and more---as special cases of one variational problem. Yet two dimensions of this space remain entirely unexplored: the interaction term

\mathcal{I}

is set to zero in many existing models, and the rich family of MFG solvers has never been applied to generative modeling. We address both gaps with MFGLab an open-source PyTorch library whose primary API is the cost tuple: all twelve models are specified by four composable cost functions, and the training loop, log-Jacobian, and reverse-ODE sampler are shared automatically. We additionally propose DI-Flow, a novel cost design that uses a differentiable entropy functional to encourage mode coverage, and provide learning-based MFG solvers that substantially outperform neural training on stochastic-dynamics rows. Experiments on two 2-D benchmarks confirm that the unified API is lossless relative to hand-coded implementations.

Kun Zhao, Xu Chen

Mean Field Games Generative Modeling Flow-Based Generative Modeling

Jul 23, 2026cs.LG

Expanding Flow Maps

Flow-based generative models have enabled remarkable progress in fast and controllable generation across continuous and discrete state spaces, yet existing parameterizations are constrained to fixed dimensions or fixed sequence lengths. Here, we introduce Expanding Generative Flows (EFlows), which define flows between distributions of increasing dimensionality along an expanding interpolant that grows the state by augmenting it with conditional noise. Building on this construction, we propose Expanding Flow Maps (EFMs), a new class of flow maps that distill the expanding interpolant into efficient few-step generative models. Each EFM factors the map between any two timesteps into two learnable operations: an expand operator, which augments the state space with new coordinates or tokens conditioned on the current state, and a transport map, which pushes the expanded state forward along the interpolant. Composing these operators yields a single map that jointly expands and denoises the state, recovering existing fixed-canvas flows and flow maps as the special case in which the expand operator is the identity. We further extend the framework to the discrete simplex, enabling variable-size graph generation and variable-length sequence generation. Across both continuous and discrete modalities, we establish EFlows and EFMs as a principled framework for settings in which output size is itself a learned, controllable degree of freedom.

Sophia Tang, Pranam Chatterjee

Department of Computer and Information Science, University of Pennsylvania · Department of Bioengineering, University of Pennsylvania

Flow Map Learning Generative Modeling Flow-Based Generative Modeling

Jul 21, 2026cs.CV

Latent Riemannian Flow Matching for Geometry-Grounded 3D Foundation Models

Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support. Generative models for 3D scenes, on the other hand, must rely on strong geometric priors to produce coherent outputs from sparse inputs. We bridge these two paradigms by performing flow matching directly in VGGT's latent space, leveraging its learned 3D priors without committing to any explicit downstream representation such as Gaussians, meshes, or video-VAE latents. This requires respecting the latent geometry: VGGT tokens occupy a product of high-dimensional hyperspheres on which standard Euclidean flow matching fails. We address this with a Riemannian Flow Matching framework defined on a product manifold of four hyperspheres, aligned with VGGT's multi-scale encoder, which keeps generated tokens on the valid data manifold required by the frozen decoding heads. On RealEstate10K, ScanNet++ and ETH3D, our method achieves strong performance against recent scene generation baselines in both per-view appearance and aggregated 3D geometry, establishing latent-space flow matching on geometric foundation models as a viable paradigm for 3D generation. The project page can be found

\href{https://lisaweijler.github.io/geometry-grounded-rfm/}{\text{here}}

.

Lisa Weijler, Irene Ballester, Guofeng Mei +2

TU Wien · Fondazione Bruno Kessler · Imperial College London

3D Foundation Models Flow Matching Riemannian Flow Matching 3D Scene Generation Generative Modeling 3D Representation Learning

Jul 21, 2026cs.LG

GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks

Equivariant graph neural networks provide a powerful modeling language for three-dimensional scientific data, but their reuse is often limited by implementations tied to specific tasks, outputs, and training regimes. We present GEqTrain, a configuration-driven framework that separates dataset semantics, model composition, and training objectives. Raw data are mapped to typed node-, edge-, and graph-level fields, while model stacks, losses, and training workflows are assembled declaratively through Hydra configurations. A shared equivariant backbone and training infrastructure can therefore be retargeted to a new task primarily through configuration. We demonstrate this flexibility on three different problems handled within one software stack: coarse-grained-to-atomistic backmapping of biomolecular systems, prediction of NMR chemical shifts in molecular solids, and equivariant generative modeling. Our aim is not to surpass individually optimized task-specific systems, but to show that a shared representation and training infrastructure can achieve competitive accuracy across qualitatively different tasks at the cost of a configuration change. We further introduce GEqDiff, a generative extension based on equivariant flow matching. GEqDiff treats user-defined equivariant fields as first-class generation targets, jointly transporting Cartesian positions and non-scalar node fields spanning representations up to l=3 within a single equivariant flow. We validate this capability on a controlled synthetic benchmark inspired by protein secondary-structure motifs, showing that fields with heterogeneous transformation properties can be reconstructed jointly and with high fidelity. By reducing the software overhead of moving between predictive and generative, scalar and tensorial settings, GEqTrain aims to make equivariant modeling more reproducible, extensible, and reusable.

Daniele Angioletti, Marco Nobile, Vittorio Limongelli

Faculty of Biomedical Sciences, Euler Institute, Universit´a della Svizzera italiana, 6900 Lugano, Switzerland

Flow Matching Generative Modeling Equivariant GNNs Equivariant Representation Learning

Jul 21, 2026cs.LG

Decafs: Disentangled Conditional adversarial Flows

Flow-based models have established state-of-the-art performance in generative modeling across domains, but are hard to interpret due to their complex latent embeddings. In particular, the entanglement of generative factors in the latent space hinders controlled generation. We circumvent this issue by appealing to a novel conditional generator based on Lie groups that disentangles an alternative latent space, which is aligned closely with the latent flow space using an adversarial loss. Our approach facilitates interpretable conditional generation while obviating the need to expand the dimensionality of the flow space (owing to its invertibility requirements). The proposed model demonstrates strong performance across conditional image (including, outperforming StyleGAN on MNIST, dSprites) and molecule (using standard QM9, ZINC and MOSES) generation tasks

Anirudh jain, Sakshi Varshney, Samuel Kaski +1

Orion Pharma · Aalto University, Finland · Aalto University +3

Disentangled Representation Learning Normalizing Flows Conditional Image Generation Generative Modeling Molecular Generation Flow-Based Generative Modeling+1

Jul 20, 2026cs.LG

SGN: A Similarity-based Generative Network for Data Generation under Distribution Shift

Generative models trained on a source domain often produce samples that are poorly aligned with shifted target domains, limiting their effectiveness for target-domain data augmentation. Although target-specific adaptation can reduce this mismatch, it typically requires additional optimization and domain-specific parameters. We propose a Similarity-based Generative Network (SGN), a reusable framework that is trained once on labeled source data and applied to new target domains without parameter updates. SGN learns a latent space structured by label-induced pairwise similarities while preserving reconstructive information through an encoder-decoder architecture. At generation time, a small labeled representative set from the target domain is encoded and combined in the learned latent space, allowing the generated samples to inherit target-specific characteristics while maintaining class consistency. We further analyze the realizability and dimensionality requirements of the proposed similarity structure. Experiments on image and tabular datasets demonstrate the effectiveness of SGN for target-guided data augmentation under source-to-target distribution shifts.

Jiaqi Zhu, Xincheng Chen, Yuncheng Wu +2

National University of Singapore · Renmin University of China · Beijing Institute of Technology +1

Synthetic Data Augmentation Generative Modeling Conditional Generative Modeling

Jul 15, 2026cs.AI

The Steering Budget: Examples beat Knobs

Generative models are steered with knobs -- prompts, guidance scales, property tags. Turn one as hard as you like and, past a point, it stops moving the property you care about. We find that ceiling is not a shortcoming of the model but a budget, set by the training data before the model is trained: a property's movable range splits in two -- the part a knob can reach, and a second, significant part that only examples -- concrete instances of what you want more of -- can reach. That second part is usually much larger, but not always, and the same budget says so in advance. Reaching that second part takes a different move: instead of turning a knob, you show the model examples, composed from what it already learned rather than added to its training. A cheap audit of the training data measures the budget; we give a recipe for building the example set that reaches all of it. This buys two things a knob can't. Reach: it moves a property across the whole budget, not just the part a knob reaches. Expressiveness: it steers toward targets you can only specify by example -- including ones you can't put into words. We turn these into a handful of falsifiable claims and verify them in two unrelated domains, image and crystal-structure generation -- marking where a knob is enough, and where only examples will do.

Raj Kumar Rajendran

Generative Modeling

Jul 15, 2026cs.LG

Heavy-Tailed Flow Matching via Random Clocks

Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes. Standard diffusion and flow-matching models typically begin from Gaussian noise or Gaussian source distributions, which yield tractable training targets but provide a poor inductive match for heavy-tailed data. We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources. Conditioning on a given clock path, the source distribution and flow are Gaussian; marginalizing over the clock gives a Gaussian scale mixture covering Gaussian,

α

-stable, and Student-t families. To make the clock-conditioned vector field practical, we encode the path-valued clock using truncated logsignature features, allowing the velocity field to adapt to the realized conditional space with negligible overhead. Empirically, on 2D imbalanced

α

-stable mixtures, CIFAR10-LT, and HRRR weather fields, HTFM improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and competitive heavy-tailed baselines, while retaining the low-NFE sampling advantage of flow matching. Moreover, the random-clock formulation further provides a practical tail-control interface: by varying only the clock law or tail parameter, the same architecture can calibrate the ``heaviness'' of generated tails across different distribution families.

Zhouhao Yang, Yezhen Wang, Kenji Kawaguchi +2

Department of Applied Mathematics and Statistics, Johns Hopkins University. · School of Computing, National University of Singapore. · Department of Computer Science, Johns Hopkins University.

Flow Matching Heavy-Tailed Noise Generative Modeling Flow-Based Generative Modeling Heavy-Tailed Distributions

Jul 14, 2026cs.LG

The Geometry of Memorization: Finite-Time Spectral Sensitivity as a Diagnostic for Flow Matching Models

Continuous-time generative frameworks construct probability paths between base and target domains by optimizing time-dependent velocity fields. While theoretical targets favor straight trajectories, empirical networks develop complex path deformations. This paper presents the Finite-Time Spectral Sensitivity (FTSS) g(t), a gradient-free, forward-pass metric that exposes flow geometry by tracking the root-mean-square singular value of the state-transition matrix. Serving as a continuous proxy for stable rank, g(t) reveals a distinct geometric pathology under data scarcity: while generalizing models maintain stable effective dimensions, overfitting causes a spectral collapse. We leverage this structural phenomenon to develop an internal geometric audit based on g(t). Our framework detects generative memorization using purely internal trajectory dynamics, removing the need for external membership queries or baseline data comparison.

Shuchan Wang

Flow Matching Neural Network Memorization Memorization in Generative Models Generative Modeling Flow-Based Generative Modeling

Jul 13, 2026cs.CV

Self-Consistent Flow: Unifying Velocity and Endpoint Prediction for Rectified Flow Models

In rectified-flow-based generative models, the neural network can be trained to predict two different targets, such as the instantaneous velocity or the data endpoint, to perform denoising. Although prior work shows that these parameterizations lead to different empirical behaviors, the mechanisms underlying their respective advantages remain to be underexplored, and how to combine them effectively is still unclear. In this work, we analyze how learning errors from different parameterizations affect the generation performance. We show that predicting the data endpoint has a clear training signal that stabilizes training, whereas predicting the velocity maintains stable sampling dynamics near the data manifold. Motivated by these insights, we propose Self-Consistent Flow (SC-Flow), a new method that unifies the benefits of both parameterizations. By employing a lightweight consistency loss, SC-Flow jointly trains a single network to predict both the local velocity and the data endpoint, and the consistency between the two predictions improves the model's performance. The method requires no major architectural changes and adds minimal computational overhead. Extensive experiments on image generation tasks demonstrate that SC-Flow substantially stabilizes optimization and improves the straightness of generation paths, leading to significant gains in generation quality over standard rectified-flow baselines.

Xu Han, Jiajing Hu, Li-Ping Liu

Department of Computer Science Tufts University

Rectified Flow Image Generation Generative Modeling Flow-Based Generative Modeling

Jul 12, 2026cs.LG

Diachronic Sample Integration: Robust Tail-Risk Estimation with Generative Models

Deep generative models are increasingly used as simulators for downstream decision-making under data scarcity, but in risk-sensitive applications their usefulness depends on rare adverse scenarios rather than typical samples. Standard generative objectives prioritize bulk distributional fidelity, leaving low-probability tails vulnerable to localized optimization noise and making tail-dependent functionals unstable under finite simulation budgets. We introduce Diachronic Sample Integration (DSI), a test-time inference framework that ensembles generated samples across checkpoints from a stochastic training trajectory. DSI targets a checkpoint-mixture distribution that averages checkpoint-specific tail fluctuations rather than relying on a single brittle endpoint. We formalize this mechanism through a finite-budget bias-variance theory. Empirically, across multivariate synthetic processes and high-frequency trading data, DSI substantially reduces tail-estimation error compared to single-checkpoint baselines under fixed simulation budgets, outperforming standard diffusion and state-of-the-art tail-aware baselines without modifying the generative objective.

Shuning Zhao, Patrick Wong, Leran Zhang +1

Department of Computer Science and Technology, BNRist, Tsinghua University, China · Department of Econometrics and Business Statistics, Monash Business School, Monash University, Australia · School of Mathematics and Statistics, University of Melbourne, Australia

Ensemble Learning Generative Modeling Rare-Event Estimation

Jul 10, 2026cs.CV

Detangled: A Framework for Creating, Editing, and Inferencing Feature Rich Hair Strands

We present a framework for understanding and generating feature rich hair strands. Drawing upon both scientific and cultural expertise, we define strand texture as the various distinctive patterns (curling, switchbacks, twist, etc.) that are formed by forces internal to a hair strand. We begin by proposing a novel five-dimensional parameter space, intended to be a bijection with naturally occurring hair strand textures. This encoding is both qualitatively accessible, allowing users to readily locate their own hair in the parameter space, and quantitatively precise, allowing the generation of individual strands from texture inputs. Importantly, strand texture should be independent from the overall strand direction. In order to disentangle strand texture from the overall strand direction, we identify centerline geometry and use it to map strands into a canonical space (a strand texture space). We construct centerlines using a novel method that cleanly distills complex hair grooms, separating the strand texture from the overall style (parameterized by style guides). We enable the creation of new strands conforming to our parametric description of texture via a generative artificial intelligence approach supervised by a separate neural network trained to label candidate strands according to our five-parameter description. The ability to create new strands conforming to any desired texture enables groom editing using either texture transfer or user-provided inputs. We demonstrate results on a variety of hair types.

Sarah Jobalia, Yitong Deng, Carolyn Smith +1

Stanford University, USA

Generative Modeling Image Editing

Jul 10, 2026cs.LG

Variable-Length Generative Protein Design via Generalized Poisson Flow

The ability to generate variable-length proteins is crucial in protein design, where the optimal length is often unknown and tightly coupled to designability. Current diffusion- and flow-based generative models typically require the protein length to be specified before sampling, limiting their flexibility in exploring the feasible design space. To address this limitation, we introduce Generalized Poisson Flow (GPFlow), a variable-length generative framework that learns the rate function of an inhomogeneous generalized Poisson process by minimizing its negative log-likelihood. We establish population-level guarantees for recovering the joint multimodal distribution and derive an upper bound on the KL divergence between the data and generated distributions. We comprehensively evaluate GPFlow across structure and sequence design, motif scaffolding, and peptide co-design, spanning Euclidean, categorical, and Riemannian modalities to fully validate its variable-length generation quality. In unconditional design, GPFlow improves structural designability and achieves the best distributional fitness for sequence design compared to their corresponding fixed-length baselines, while perfectly recovering the length distribution. In conditional motif scaffolding, GPFlow ranks first on 10 of 16 structure-based design tasks with significantly more unique successes and also achieves more passed tasks in sequence-based design. In peptide co-design, GPFlow remains competitive even without access to a native-length oracle.

Chaoran Cheng, Zhanghan Ni, Yanru Qu +4

Siebel School of Computing and Data Science University of Illinois Urbana-Champaign

Generative Modeling Flow-Based Generative Modeling Protein Design Conditional Generative Modeling

Jul 8, 2026cs.CV

DreamCharacter-1: From 3D Generative Foundation Models to Product-Ready Character Generation

We present DreamCharacter-1, a lightweight post-adaptation framework that calibrates pretrained 3D foundation models toward high-fidelity, production-ready 3D character generation. Building upon a 3D foundation backbone, our pipeline incorporates three task-oriented components: (1) geometry post-training, which enhances fine-grained surface details through geometric preference optimization; (2) texture post-training, which synthesizes high-resolution textures and refines the appearance of occluded regions; and (3) inference acceleration, which enables scalable deployment. Extensive quantitative and qualitative experiments demonstrate that DreamCharacter-1 produces visually compelling and structurally robust 3D character assets, consistently surpassing state-of-the-art character generation methods.

Weizhe Liu, Yunjie Wu, Xiangqian Shu +5

Intelligent Creation Team, ByteDance

3D Foundation Models 3D Asset Generation 3D Avatar Generation Generative Modeling Texture Synthesis

Jul 8, 2026cs.LG

Unlocking Temporal Generalization in Hamiltonian Video Dynamics Models

World models are typically trained to predict discrete-time physical dynamics with a fixed step size baked into the model weights, preventing prediction at variable temporal resolutions. This matters for hierarchical planning, sim-to-real transfer, and scientific or game-engine applications that must query the same dynamics at multiple timescales. Hamiltonian Generative Networks (HGN) offer a principled path forward, grounding predictions in a continuous-time energy function that is, in principle, independent of the observation frame rate. In practice, however, their temporal generalization breaks down in non-conservative settings. We show that in externally forced, dissipative environments, HGN rollouts at step sizes beyond the training regime fail due to distinct failure modes, including latent magnitude growth driven by an unconstrained action-force map, and global truncation error accumulation from an under-resolved integrator. We identify a targeted fix for each mechanism and demonstrate stable dynamics prediction at temporal resolutions well outside the training distribution. In a detailed analysis, we recommend several strategies for enabling temporal generalization in continuous-time video generation.

Eli Laird, Corey Clark

Department of Computer Science, Southern Methodist University, Dallas, TX, USA

Physical Consistency in Video Generation Latent Dynamics Modeling Hamiltonian Neural Networks Generative Modeling Temporal Consistency in Video Generation Hamiltonian Dynamics

Jul 8, 2026cs.LG

BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces

Bubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble-bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate a permutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems.

Rachna Ramesh, Kiet Bennema ten Brinke, Douwe Orij +2

Department of Mathematics and Computer Science, Eindhoven University of Technology · Department of Chemical Engineering and Chemistry, Eindhoven University of Technology

Generative Modeling Spherical Harmonics Trajectory Prediction Computational Fluid Dynamics

Jul 7, 2026cs.LG

From Jumps to Signatures: a Generative Method for Temporal Point Processes

Rough path signatures are a universal feature map for continuous paths and, via the expected signature, characterise path distributions. These guarantees do not directly extend to cadlag paths of Temporal Point Processes (TPPs), limiting the use of signature methods for event sequences. Furthermore, neural TPP models, including recent generative approaches, optimise per-event objectives with no global sequence-level loss, while evaluation of variable-length event sequences lacks distributional discrepancy measures. This paper proposes a common pathwise framework for addressing these limitations. We introduce the interarrival embedding, a stable, injective lift from jump paths to continuous paths of bounded variation, extending signature methods to discrete event sequences. Our theoretical contributions give rise to sigTPP, the first signature-based generative model for TPPs, trained using a path-level loss on complete trajectories. We further analyse the space of counting paths and derive three distributional discrepancies, providing mathematically justified tools for evaluating generative TPP models. Across synthetic and real-world datasets, sigTPP achieves the best average rank based on eight complementary metrics, outperforms or is within a standard error of the strongest baseline in 64% of the dataset-metric pairs, and according to a relative score, improves against every baseline by at least 19% on average.

Niels Cariou-Kotlarek, Vasileios Lampos

Centre for Artificial Intelligence Department of Computer Science University College London

Temporal Point Processes Generative Modeling

Jul 7, 2026cs.LG

Decision-Focused Scenario Generation and Selection for Efficient and Robust Grid Dispatch

The increasing uncertainty from flexible demand and renewable generation has made distributionally robust optimization (DRO) an important tool for robust power system dispatch. DRO relies on forecast scenarios to construct ambiguity sets, but conventional scenario generation pipelines are often trained in an accuracy-oriented manner and may neglect spatial correlations among uncertainties. This mismatch can produce ambiguity sets that are statistically plausible but suboptimal for downstream operation. This work proposes a decision-focused generative framework for correlated scenario generation in DRO-based dispatch. Instead of training generative models solely to fit the historical uncertainty distribution, the proposed framework optimizes generated scenarios according to their induced downstream operational cost. The proposed framework is tailored to mainstream generative models, including variational autoencoders, generative adversarial networks, and diffusion models, while capturing the joint distribution of uncertainties across buses. To improve computational tractability, we further develop a differentiable scenario selector that selects decision-relevant scenarios from a generated pool and can be trained within the same decision-focused pipeline. Case studies demonstrate that the proposed framework effectively reduces 0.80%-2.02% operational cost across different generative models compared to accuracy-oriented methods.

Yangze Zhou, Yihong Zhou, Thomas Morstyn +1

Distributionally Robust Optimization Decision-Focused Learning Generative Modeling Decision-Making under Uncertainty Power Systems

Jul 5, 2026math.OC

Constrained Flow Matching via Lagrangian Dual Flows

Flow matching is a powerful tool for generative modeling, but emerging applications in robotics, planning, and control require inference-time constraints on generated outputs. Such constraints are often complex and highly nonlinear. As a result, methods designed for linear constraints like image inpainting are rarely sufficient, and projection or optimization-based alternatives can be prohibitively expensive. In this paper, we introduce Lagrangian Dual Flows, a new family of constrained generation techniques based on Lagrangian dual dynamics. By flowing a dual co-state alongside generated samples, we can guarantee nonlinear constraint satisfaction without expensive optimization subproblems, pseudoinverses, or projection steps during the denoising process. The resulting constrained generation algorithms are simple, effective, and open new theoretical connections between flow matching and primal-dual methods in numerical optimization.

Vince Kurtz, Alexander Davydov

DePaul University · Rice University

Constrained Generative Modeling Flow Matching Generative Modeling Constrained Optimization Flow-Based Generative Modeling

Jul 5, 2026cs.LG

One Framework for All: Cross-Modal Membership Inference for Generative Models

Large generative models across text-to-text, text-to-image, and image-to-text modalities have been shown to pose significant privacy risks. One fundamental threat is membership inference attacks (MIA), which aim to determine whether a given data point was used in a model's training set. Although prior work has investigated MIAs against these three classes of generative models, existing approaches treat them in isolation and are not cross-applicable, thereby limiting their real-world utility. To address this limitation, we present the first comprehensive study of a unified membership inference framework that applies across text-to-text, text-to-image, and image-to-text modalities. Our approach is grounded in a key modality-agnostic observation: the output distribution of a generative model can approximate its training data distribution. Leveraging this property, we model the distributions of model-generated outputs and auxiliary non-member samples in a shared embedding space, and perform membership inference via likelihood ratio testing. We conduct extensive experiments in a strict black-box setting under both partial-knowledge and zero-knowledge threat models, and evaluate membership inference against both fine-tuning and pre-training data. Experimental results demonstrate our approach's superior performance in comparison to existing state-of-the-art methods, which are typically optimized for a single model class.

Dayong Ye, Tainqing Zhu, Kun Gao +6

Dayong Ye, Tianqing Zhu∗, Kun Gao, Junhao Liu, Yichuan Chen, Shuai Zhou, Hengzhu Liu, Bo Liu, and Wanlei Zhou

Membership Inference Attacks Generative Modeling

Jul 3, 2026cs.LG

Reflected Schrödinger Bridge Matching

Recent advances in generative modeling have enabled the efficient computation of Schrödinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching. However, these have not covered SBs with reflecting dynamics, a useful model choice with built-in guarantees that generated samples stay in the data domain. Existing alternatives for reflected SBs instead rely on more complex training based on forward--backward SDE theory, requiring expensive higher-order derivatives and sampling entire paths during training. In this article, we introduce a partially simulation-free framework that allows reflected SBs to be trained similarly to flow matching, using a new sampling method and regression target. We demonstrate our results by coupling pairs of well-known high-dimensional image datasets. Using reflected dynamics incurs negligible additional wall-clock time during both training and inference while maintaining or slightly improving generative performance.

Marcus Häggbom, Viktor Nilsson, Pierre Nyquist +1

SEB Group and Department of Mathematics KTH Royal Institute of Technology Stockholm, Sweden · Department of Mathematical Sciences Chalmers University of Technology and University of Gothenburg and Department of Mathematics KTH Royal Institute of Technology

Schrödinger Bridges Image Generation Generative Modeling

Jul 3, 2026physics.chem-ph

AquaGen: Scaling generative models to molecular dynamics precision on thousands of atoms

We present AquaGen, the first all-atom, explicit solvent, periodic-boundary-condition-aware generative model that produces molecular configurations from the Boltzmann distribution at a fraction of the cost of molecular dynamics (MD). This is in contrast with existing generative models that remove degrees of freedom by operating on coarse-grained, vacuum, or implicit solvent systems. Operating at this resolution allows for post-processing through force field energy evaluations and MD simulations, and enables the prediction of relevant properties in a gray-box manner (as ensemble averages of potential energy evaluations over generated samples). We demonstrate the utility of this paradigm on absolute hydration free energy (AHFE), producing estimates 4-10x faster and with comparable accuracy to standard GPU-based MD. By generating uncorrelated samples from alchemical Boltzmann distributions, we create more accurate, interpretable, and refinable ensemble predictions with calibrated uncertainty estimates, unlike regression methods which are entirely black-box predictors. Our approach also yields predictable benefits from increasing train- and test-time compute, realized by scaling model size and generating more samples, respectively. We believe that this approach demonstrates the utility of high-resolution ensemble generation for free energy estimation, with future potential to replace MD in tasks such as the prediction of lipophilicity, membrane permeability, or absolute binding free energy (ABFE) -- whose grounding and interpretability may be critical for the development of new drugs and materials.

Emmanuel Bengio, Sanjeev Raja, Yui Tik Pang +5

Valence Labs · Recursion · UC Berkeley

Free Energy Calculation Generative Modeling Molecular Generation Molecular Property Prediction

Jul 2, 2026cs.CV

SAMoR: Motion Modelling for Articulated Objects of Any Skeleton and Topology

Modeling motion for articulated objects of arbitrary skeleton topology remains difficult: existing motion generators target a fixed human skeleton, and prior adaptations either fail to share a vocabulary across rigs or discard motion detail through global pooling. Our key observation is that while joint-level motion does not correspond cleanly across species, motion of functional joint groups does: a human arm, a wolf foreleg, and a bird wing share motion structure despite differing joint counts and connectivity, a correspondence that joint names (e.g., "forearm", "wing_L1") partially expose even when topology does not. We introduce SAMoR (Skeleton-Aware Motion Representation for Articulated Objects), a cross-topology motion representation that encodes each motion segment as a small fixed number (

K=8

) of part tokens shared across arbitrary skeletons. A graph-transformer encoder consumes per-joint motion features, kinematic graph structure, and joint-name embeddings, then compresses them into part-level tokens via cross-attention pooling and residual vector quantization, yielding a discrete motion codebook shared across rigs. To keep the part queries from collapsing into redundant global representations, we introduce a topology-agnostic attention supervision loss, with joint-name dropout to reduce over-reliance on text labels. We curate a heterogeneous corpus from HumanML3D, Truebones Zoo, and animated Objaverse-XL assets, and evaluate SAMoR on held-out characters with unseen skeletons. It supports accurate reconstruction and cross-topology transfer, and enables text-conditioned generation and part-wise editing via a MaskGIT token generator. SAMoR reaches

2.75 \times 10^{-2}

normalized MPJPE on cross-topology reconstruction,

5.8\times

below the strongest adapted variable-

J

tokenizer baseline, while remaining competitive with fixed-skeleton specialists on HumanML3D.

Yuhao Zhang, Gerard Pons-Moll, Tolga Birdal

Imperial College London · University of Tübingen, Tübingen AI Center

Generative Modeling Motion Representation Learning

Jul 1, 2026cs.LG

Decision-Aware Training for Sample-Based Generative Models

Sample-based generative models are increasingly used for probabilistic forecasting in high-stakes decision settings, yet their training objectives are blind to the decision maker's cost structure. These models are commonly trained with strictly proper scoring rules, such as the energy score, which allocate their training signal in proportion to data density, with no awareness of where forecast errors are most costly for downstream decisions. We therefore propose decision-aware training for sample-based generative models, augmenting the energy score objective with a differentiable decision loss that directly penalises the cost incurred by acting on the model's forecast. This combined loss is theoretically grounded, as the decision loss is itself a proper scoring rule. We validate our method on one synthetic and two real-world tasks, showing targeted improvements in cost-sensitive regions while retaining full probabilistic forecasts.

Kornelius Raeth, Nicole Ludwig

T ubingen AI Center, University of T ubingen, Germany · University of Augsburg, Germany

Cost-Sensitive Learning Probabilistic Forecasting Decision-Focused Learning Proper Scoring Rules Generative Modeling

Jul 1, 2026cs.CV

GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models

We introduce GenSP, a data-driven framework that learns consistent spherical parameterizations across a collection of genus-0 shapes. Instead of optimizing the parameterization of each shape independently, our method learns a neural generative model that predicts a continuous mapping from the unit sphere to shapes in a dataset. Under this formulation, spherical parameterizations are obtained through the inverse mappings of the learned generator, which encourages similar shapes to share consistent parameterizations. To make this formulation practical, we address several key challenges in learning such a generative model. First, we introduce a continuous neural deformation model that predicts surface points from sphere coordinates and latent shape codes, avoiding discretization artifacts common in mesh-based formulations. Second, we augment the training space with intermediate shapes that bridge the sphere and input shapes, allowing the model to learn meaningful deformations across a heterogeneous shape collection. Third, we compute reliable initial correspondences by propagating mappings along a spanning tree of training shapes in the latent space. Experiments on the ShapeNet dataset demonstrate that our approach significantly reduces geometric distortion and improves cross-shape consistency compared with state-of-the-art spherical parameterization methods.

Sai Karthikey Pentapati, Shashank Gupta, Rajesh Sureddi +3

The University of Texas at Austin · University of Colorado Boulder

Generative Modeling

Jul 1, 2026cs.LG

Generative Modeling of Quantum Distribution with Functional Flow Matching

The emergence of powerful deep generative models based on diffusion and flow matching has enabled the learning and modeling of complex distributions. Learning quantum distributions, however, remains challenging due to the inherent difficulty of accurately modeling the meaningful physical properties of quantum states. We propose Quantum Flow Matching (QFM), a novel generative model designed to learn quantum distribution by utilizing spin Wigner function and flow matching. By converting density matrix into the spin Wigner function and leveraging functional flow matching to learn distributions in function space, QFM enables accurate and effective learning of multi-qubit quantum distributions. We demonstrate the effectiveness of our method by evaluating physical quantities such as trace, purity, and entanglement entropy of the generated quantum states, accurately capturing the underlying physics of the given quantum distributions.

Jaehoon Hahm, Tak Hur, Joonseok Lee +1

Department of Statistics and Data Science, Yonsei University, Seoul, Korea · Graduate School of Data Science, Seoul National University, Seoul, Korea · Google Research, Mountain View, California, United States +1

Flow Matching Quantum Generative Modeling Quantum Machine Learning Generative Modeling

Jun 30, 2026cs.LG

TRIE: An Evaluation Framework for Stochastic PDE Surrogates

Many scientific systems exhibit uncertainty from stochastic forcing, unresolved degrees of freedom, or imperfect observations, making reliable surrogate forecasting fundamentally distributional rather than pointwise. For such systems, deterministic neural surrogates fail to capture statistical measures and forecast uncertainty. We introduce TRIE, an evaluation framework for stochastic PDE surrogates that asks whether models reproduce invariant measures, provide trustworthy predictive uncertainty, and scale to efficient probabilistic generation. We demonstrate TRIE on two stationary chaotic spatially extended SPDEs, stochastic Kuramoto--Sivashinsky and stochastic Kolmogorov flow, across 11 parameter values. Our evaluation shows that standard pointwise-trained neural surrogates can produce plausible short rollouts while failing to match long-time statistical structure. Approximate uncertainty methods such as Monte Carlo dropout and heteroscedastic Gaussian likelihoods produce stochastic forecasts, but are often miscalibrated and overconfident under temporal and spatial uncertainty diagnostics. Across these criteria, generative models provide the most consistent performance, accurately capturing invariant measure statistics and achieving the lowest CRPS in all reported probabilistic settings. Finally, we show that latent generative models with automatic dimension discovery retain much of this statistical fidelity while reducing Kolmogorov inference time by roughly

12\times

. We release our code and data at https://github.com/scailab/TRIE-SPDE-Bench to support reproducible evaluation of stochastic PDE forecasting models.

Bharat Srikishan, Javier E. Santos, Nikhil Muralidhar +1

Stevens Institute of Technology · Los Alamos National Laboratory

PDE Surrogate Modeling Probabilistic Forecasting Generative Modeling Uncertainty Calibration

Jun 30, 2026cs.LG

SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling

Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics. Constrained sampling closes this gap, enforcing such constraints exactly at inference time without retraining, but at a computational cost: projection, correction and trajectory-optimization steps are repeated during sampling, with these steps becoming expensive for nonlinear constraints. Standard ML frameworks exacerbate this: their dense tensor algebra and limited sparse solver composability obscure the structure that physical constraints naturally induce, making efficient batched nonlinear optimization difficult to realize in practice. We address this bottleneck by exploiting the structure that sample-wise batching and local PDE couplings induce in the projection subproblems -- namely, block-sparse Jacobian and KKT systems -- exposing this structure using ExaModels.jl and solving the resulting sparse nonlinear programs with MadNLP.jl and GPU sparse factorization. Applied to Physics-Constrained Flow Matching (PCFM), on PDE benchmarks with linear, nonlinear, one-dimensional, and two-dimensional constraints, this approach accelerates nonlinear constraint projection while maintaining constraint satisfaction. These results show that sparse GPU nonlinear optimization is a practical foundation for constrained generative sampling in scientific machine learning.

Alaina Kolli, Theodoros Xenakis, Utkarsh Utkarsh +4

Massachusetts Institute of Technology, Cambridge, MA, USA · Norwegian University of Science and Technology, Trondheim, Norway

Constrained Generative Modeling Physics-Informed Generative Modeling PDE Surrogate Modeling Generative Modeling Constrained Optimization Flow-Based Generative Modeling

Jun 30, 2026cs.CV

Deep Spectral Models for Robust Dental Shape Generation

Accurate modeling of dental crown morphology is fundamental for diagnosis, orthodontic planning, and computer-aided restoration design. However, datasets suitable for training such models are typically limited in size. We present ToothForge, a deep spectral generative framework that models dental crown geometries from compact, intrinsic representations. By operating in the spectral domain, ToothForge learns a latent manifold of 3D tooth shapes through synchronized spectral embeddings, ensuring consistent modeling across samples with varying connectivity. Spectral synchronization mitigates the instability of Laplace-Beltrami eigenbases and enables efficient learning in a low-dimensional space. The framework is thoroughly evaluated through robustness analysis, ablation studies, and benchmarking against PCA-based statistical shape models and point-based generative frameworks. Results show that synchronized spectral modeling achieves reconstruction and generative performance comparable to or exceeding spatial approaches, while maintaining compactness and geometric interpretability. Together, the compact synchronized coefficients and low-dimensional learning space make the framework particularly suitable for limited datasets, as often encountered in dental and medical domains, and applicable in real-world scenarios where guaranteeing consistent connectivity across shapes from various clinics is unrealistic.

Tibor Kubík, François Guibault, Michal Španěl +1

Polytechnique Montr´eal, Montr´eal, Canada · Brno University of Technology, Brno, Czech Republic

Geometric Representation Learning Generative Modeling 3D Shape Generation