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.

Jul 13Week of Sep 28

Latest papers 347

Sep 28, 2026cs.LG

FAST-Brain: A Flow-Aligned Spatio-Temporal Surrogate Brain Model

Modeling resting-state functional magnetic resonance imaging (rs-fMRI) data is crucial for understanding brain-wide neural activity. However, traditional methods struggle to capture complex temporal dynamics over long horizons, to account for the brain's anatomical spatial structure, and to model high-dimensional ambient signals that lie on a low-dimensional intrinsic subspace. We propose FAST-Brain, a unified flow-aligned spatio-temporal surrogate brain model that addresses all three challenges. At its core is a flow-aligned generative framework that directly predicts the clean blood-oxygen-level-dependent (BOLD) signal, paired with a graph convolutional network that captures spatial structural constraints and a Transformer that models long-range temporal dependencies. Theoretically, we show that under a low-dimensional subspace assumption, the approximation error of our model scales with the intrinsic dimension rather than the ambient dimension, which justifies our direct modeling of the BOLD signal. Extensive experiments on synthetic and Human Connectome Project datasets demonstrate that FAST-Brain achieves state-of-the-art performance in recovering functional connectivity, effective connectivity, and the implicit low-dimensional signal subspace.

Shucheng Liu, Changchun Shi, Kai Zhang +1

University of North Carolina at Chapel Hill · London School of Economics and Political Science

Neural Surrogate Modeling Functional Connectivity Generative Modeling Flow-Based Generative Modeling Neuroimaging Spatiotemporal GNNs+1

Sep 28, 2026cs.CV

Scaling Versatile 3D Assets Editing with a Million-Scale Dataset

Although recent 3D generative models produce increasingly realistic assets, controllable 3D asset editing remains challenging. Existing methods are limited by scarce training data, insufficient source-aware modeling, and a lack of practical evaluation protocols. To address these limitations, we present Alchemy3D, a unified framework for training and evaluating versatile 3D asset editors that covers data construction, model architecture, and benchmark evaluation. Specifically, we curate Alchemy3D-1M, a large-scale 3D editing dataset containing 1.25M assets and 1.38M editing pairs across seven editing types. On this data, we train a family of generative flow models for general-purpose 3D asset editing. The model family supports image- and text-conditioned editing, few-step inference, and transfer to multi-view 3D part segmentation. We further introduce GEdit3D-Bench, a large-scale, open-world benchmark with a multi-dimensional evaluation protocol. Across existing and newly introduced benchmarks, our method outperforms prior methods on most metrics of editing fidelity, source preservation, and visual quality.

Badi Li, Tianxin Huang, Yu Zhou +3

The University of Hong Kong · Shenzhen Loop Area Institute · Sun Yat-Sen University +1

3D Asset Generation Generative Modeling

Sep 27, 2026cs.LG

JIVE: Jacobian-Informed Volume Expansion for Diverse Generative Sampling

Generative models often suffer from mode collapse and limited sample diversity. While prior works attempt to mitigate this by jointly generating a batch of samples and repelling their trajectories, these heuristics do not explicitly maximize the diversity of the resulting endpoints. We introduce JIVE, a training-free framework that enhances generative diversity by injecting velocity perturbations aligned with the leading right singular subspace of the generator's endpoint Jacobian. By leveraging this local geometric structure, JIVE provably maximizes endpoint diversity while preserving sample quality. To maintain practical efficiency, we compute these perturbation directions via matrix-free iterations rooted in classical numerical linear algebra, requiring only a small computational overhead. Across different benchmarks, JIVE boosts both pixel and feature-level diversity in few-step and one-step generation.

Guangxun Zhang, Brian Cai, Boxuan Zhang +2

New York University · Stony Brook University · Rutgers University

Generative Modeling

Sep 27, 2026cs.LG

Source Anchoring for Physical Consistency in Flow Matching Models

Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.

Giulia Romoli, Filippo Ruffini, Paolo Soda

Department of Diagnostics and Intervention, Ume˚a University, Sweden · Unit of Artificial Intelligence and Computer Systems, Universit`a Campus Bio-Medico di Roma, Italy

Constrained Generative Modeling Physics-Informed Generative Modeling Flow Matching Generative Modeling Flow-Based Generative Modeling

Sep 27, 2026cs.LG

KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots

Learning population dynamics from temporally sparse, unpaired distribution snapshots is a fundamental challenge in developmental biology. Recent approaches based on neural differential equations and flow matching can interpolate between observed population snapshots, but may struggle to extrapolate beyond the training horizon and often lack an explicit mechanism for modeling developmental branching. We propose KoopCell, a unified generative framework based on Koopman-Mori-Zwanzig theory that jointly learns representations and predictive linear latent dynamics. Theoretically, using the weak continuity equation, we derive a closed-form least-squares estimator for the Koopman generator from distribution snapshots and establish convergence guarantees under suitable assumptions. To model branching dynamics, we further develop KoopCell-M, which incorporates non-Markovian memory into the latent Koopman dynamics through a Markovian embedding. Experiments on synthetic systems and three scRNA-seq datasets demonstrate the ability of our framework to recover Koopman spectra, model branching through memory, and scale to predicting high-dimensional gene expression distributions, achieving state-of-the-art performance among the evaluated methods.

Wanfeng Lu, Yutong Zhang, Keyi Zhou +3

School of Mathematical Sciences, SCMS, SCAM, and CCSB, Fudan University, China · Research Institute of Intelligent Complex Systems, Fudan University, China · State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institutes of Brain Science, Fudan University, China +1

Koopman Operator Learning Latent Dynamics Modeling Generative Modeling Single-Cell Transcriptomics

Sep 22, 2026cond-mat.mtrl-sci

Topology-Stratified Materials Discovery with A Flow-Based Generative Model

Accurate generation of crystal structures is the foundation to the discovery of high-performance materials for extreme-environment applications, such as aerospace, additive manufacturing, and fusion energy systems. Although generative modeling has emerged as a promising approach for crystal design, its performance remains limited by the complex crystal structures and diverse chemical compositions. In this work, we develop UFO-MGen, a universal flow-based generative model that learns topological features of Wyckoff representations and leverages this information to accurately generate crystals across vast structural and chemical spaces. Compared with state-of-the-art generative models, UFO-MGen achieves the highest crystal generation success rate under a rigorous multi-stability evaluation framework, the highest SUN (stable, unique, novel) rate, and a remarkable extrapolation capability that has not been reported by previous models. Furthermore, a fine-tuning module is implemented to UFO-MGen for property-constrained crystal generation, enabling the inverse materials design toward target properties. The UFO-MGen opens a new avenue for accelerated materials discovery and providing a foundation for universal materials intelligence.

Jingyi Zhou, Oyshee Chowdhury, Noah Oyeniran +1

Department of Aerospace Engineering and Mechanics, University of Alabama, Tuscaloosa, 35487, Alabama, United States. · Alabama Materials Institute, The University of Alabama, Tuscaloosa, 35487, Alabama, United States.

Materials Science Generative Modeling Crystal Structure Generation Flow-Based Generative Modeling

Sep 22, 2026cond-mat.mtrl-sci

Deep Generative Crystal Structure Prediction: A Benchmark Study and a Controlled Test of Prototype Dependence

Deep generative models are widely reported to enable de novo crystal structure prediction (CSP), but their capability has not been measured consistently against template-based methods. We evaluate 12 representative generative CSP models, spanning latent-variable, diffusion, flow-matching, autoregressive, and manifold random-walk architectures, against TCSP 2.0 on 180 test structures and a leakage-controlled subset of 46. All methods use identical structure-matching, symmetry, and consensus criteria. Template retrieval is the strongest single method, reaching 68.3% top-1 success; symmetry-aware EquiCSP (66.4%) and Uni-3DAR (62.9%) form the next tier. However, comparison with TCSP 2.0 shows that most structures correctly predicted by generative models are also correctly predicted by template substitution. Thus, the set of structures uniquely reachable by generation is small, limiting its practical advantage for discovering structures outside existing prototype libraries. To test the source of this performance, we removed entire stoichiometric prototype families from the training set and retrained the strongest generative model. Accuracy declined by 50-78% across four families, establishing that performance is substantially prototype-dependent. A small minority of structures survived removal of their prototype family, demonstrating a real but limited retrieval-independent predictive capacity. Present generative CSP models therefore function largely as implicit, softer-edged prototype libraries rather than genuinely de novo predictors. Enlarging this residual capacity, rather than aggregate match rate alone, is the central open problem.

Lai Wei, Rongzhi Dong, Ying Feng +2

Department of Computer Science and Engineering University of South Carolina Columbia, SC 29201 · Department of Computer Science and Cybersecurity, University of North Georgia, Dahlonega, GA 30597

Crystal Structure Prediction Generative Modeling Crystal Structure Generation

Sep 22, 2026quant-ph

Bridge of $Ψ$ 's: Quantum Circuit Optimization with Schrödinger Bridges

Quantum circuit optimization replaces a circuit with an equivalent one of fewer gates and lower depth, reducing execution cost and error rate. We ask whether a generative model can learn this transformation directly from examples, rather than selecting from a fixed rewrite library or rigid algebraic routines. We present Bridge of

Ψ

's (BOPS), a generative model based on Schrödinger bridges, using a custom denoiser architecture, that learns a transformation from a source circuit into an equivalent optimized circuit. We train it on data constructed to be hard for existing optimizers, by applying rewrite rules backwards so that each input has a known lower-cost target. On held-out 8 qubits

\times

64 depth Clifford+

T

circuits, BOPS reduces gate count by

2.46\times

and depth by

2.45\times

in geometric mean, outperforming all nine baseline optimizers. This constitutes the first generative model bridging quantum circuits and frontier machine learning methods, opening up the quantum compilation stack to learned optimization along multiple axes.

Lino S. Hofstetter, Lia Yeh, Prakash Murali

ETH Zürich Zürich, Switzerland · University of Cambridge Cambridge, United Kingdom

Quantum Circuit Compilation Generative Modeling

Sep 22, 2026cs.LG

When Riemann flows with Wasserstein: Generative Modeling of Probability Distributions on Manifolds

Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: distributions over probability measures on non-Euclidean domains. Existing generative methods largely assume Euclidean geometry and fail to capture this structure. We introduce Riemannian Wasserstein Entropic Flow Matching (RWEFM), a generative framework on the Wasserstein space

\mathcal{P}_2(\mathcal{M})

of a Riemannian manifold

(\mathcal{M},g)

. RWEFM is trained by regressing a neural vector field onto Riemannian optimal transport velocities, using McCann displacement interpolations as conditional paths. We confirm theoretically that this construction leads to a valid flow matching approach on

\mathcal{P}_2(\mathcal{M})

and introduce the Riemannian Entropic Map, a GPU-efficient approximation of the optimal transport map on manifolds. Our experiments show that by respecting the intrinsic geometry of the data, RWEFM can generate whole single-cell samples in hyperspherical latent spaces and protein conformational ensembles on the torus. As RWEFM requires only a geodesic distance and a projection operator, it is not restricted to manifolds with closed-form geometry, which we demonstrate by generating distributions on a general triangulated mesh.

Doron Haviv, Edward De Brouwer, Rishabh Anand +4

Genentech Inc., South San Francisco, CA. · Yale University, New Haven, CT.

Riemannian Flow Matching Generative Modeling Flow-Based Generative Modeling Optimal Transport

Sep 21, 2026stat.ML

Empirical Auditing of Edge-Private Graph Generators

We empirically audit privacy leakage by testing whether outputs from edge-neighbouring inputs remain distinguishable, using statistically valid lower bounds on the privacy loss witnessed by our attacks. Our framework compares direct-edge, local-structural, and GNN-based attacks through the geometry surrounding a target edge. Experiments across two generators and two networks show that privacy leakage is both mechanism- and network-dependent, with learned representations revealing information not captured by conventional local statistics.

Anum Fatima, Stratis Limnios, James Adams +4

Department of Statistics University of Oxford Oxford, United Kingdom · Plenitude Consulting, London, United Kingdom · National Physical Laboratory Teddington, United Kingdom +3

Privacy Auditing Edge Inference Generative Modeling Differential Privacy Gaussian Differential Privacy

Sep 20, 2026cs.LG

A discrete generative model of neuronal spiking activity on microelectrode arrays

Generative models of neural activity could help characterize tissue dynamics, compare experimental conditions, and simulate population activity for applications ranging from disease and drug-response studies to closed-loop experimentation. Existing approaches, however, typically assume a fixed set of sorted neurons, whereas high-density microelectrode arrays produce extremely sparse, array-wide binary spike volumes in which the observed subset of electrodes varies across assays. We introduce a discrete generative model that represents this activity using a shared vocabulary of spatiotemporal motifs. A residual vector-quantized autoencoder learns the motif vocabulary, while a factorized masked transformer predicts where activity occurs and which motif appears at each active location. We evaluate the model on 31 assays spanning human brain organoids and acute \emph{ex vivo} human hippocampal tissue. The learned motifs are broadly reused: assay identity explains only

9%

of the entropy in motif use, and motif overlap across tissue types is comparable to overlap within them. When representation quality is evaluated independently of the generative prior, our approach achieves

5.2\times

the voxel-level reconstruction average precision of a matched flat tokenizer. For masked completion and free generation, the full model achieves

1.4

--

2.6\times

the site-level average precision of the matched generative baseline and outperforms it across all four families of generation metrics. These results establish a compact, reusable representation for array-wide spiking activity without learned assay-specific parameters, providing a scalable foundation for generative modeling across diverse neural preparations.

Md Sayed Tanveer, Mohammed A. Mostajo-Radji, Ge Wang

Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA · Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute · Genomics Institute, University of California Santa Cruz, Santa Cruz, CA 95064, USA

Generative Modeling

Sep 20, 2026cs.CV

SewFusion: Tailored Generation of Topology and Panel-Level Geometry for Sewing Patterns

Generating sewing patterns from images and text requires modeling a heterogeneous representation composed of discrete topology and continuous geometry. Existing methods mainly follow two paradigms: diffusion-based methods enable holistic geometry generation by converting the entire pattern into a continuous representation, but weaken discrete topology modeling; in contrast, autoregressive methods preserve discrete topology through next-token prediction, but tie continuous geometry regression to token-level hidden states with limited panel-level context. To bridge this gap, we propose SewFusion, a unified autoregressive framework that adopts tailored generation mechanisms for discrete topology and panel-level continuous geometry, using next-token prediction for the former and flow matching for the latter. To support panel-level continuous geometry generation, we introduce a Panel Geometry VAE that learns a fixed-size latent space for variable-length panel geometry, together with Panel Geometry Flow for latent generation. We further propose Panel-Forcing to reduce the training--inference mismatch in topology context and improve robustness to topology prediction errors. Extensive experiments on SewFactory and GCD-MM demonstrate that SewFusion consistently outperforms previous state-of-the-art methods across various settings, achieving +6.36% Panel Accuracy, +11.30% Stitch Accuracy, and -1.90 Vertex L2 error in the image-text-based generation setting.

Jiaxin Lin, Xiao Pan, Hangjie Yuan +3

Digital Creative Technology Laboratory, Shenzhen University · Zhejiang University

Generative Modeling Autoregressive Generation

Sep 16, 2026eess.SP

Stable Filters for Generative Modeling of Graph Signals

Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While recent graph-aware Schrödinger bridge models incorporate topology information directly into their reference dynamics, it is unclear how perturbations of the graph propagate through these dynamics and affect the resulting generated distributions. In this paper, we analyze the structural stability of graph-aware continuous-time generative models whose drift combines a graph filter with a learned graph neural network. We derive explicit Wasserstein stability bounds that quantify the effect of relative graph perturbations on the generated distributions. Motivated by these bounds, we introduce a principled framework for designing stable graph filters that preserve the smoothing behavior of graph heat diffusion, while boosting structural stability. Experiments on synthetic and fMRI signals show our stable filters enhance structural robustness while matching or exceeding the generative quality of the heat equation baseline.

Martin Schmidt, Gonzalo Mateos

University of Rochester, Rochester, NY, USA

Graph Signal Processing Algorithmic Stability Generative Modeling

Sep 16, 2026cs.LG

When Edit Flows are Edit Jumps: replicating Edit Flows and EvoFlows

Antibody lead optimization calls for a small, bounded set of edits to an existing candidate: substitutions, but also insertions and deletions. Edit-based generative models are the only ones that allocate such an edit budget without fixing the edit positions, the edit count, or the output length in advance. However, the existing approaches Edit Flows and EvoFlows did not release code or complete training specifications. Here, we show that both methods follow the same underlying process -- edits firing one at a time, at learned rates, in continuous time -- the pure-jump case of generator matching over finite sequences. With EditJumps we introduce the first open implementation of this framework, with a single generalist antibody editor trained on 1.66M Observed Antibody Space homolog pairs to propose homolog-like variants of a seed sequence, editing unseen leads zero-shot, without the per-family retraining original approaches require. Replicating this system from scratch exposes why open code is essential for generative biology: reconciling published edit distributions required reverse-engineering an undocumented rate-scaling hyperparameter that dictates realized mutation counts. Moreover, we show that published evaluation metrics are highly sensitive to reference sample size, frequently flipping method rankings. We release our full codebase, automated test suite, and configurations at: https://github.com/VisiumCH/editjumps

Gabriel Bénédict, Melanie Buechler, Gerard Riera-Solà +3

Visium, Switzerland

Generative Modeling Protein Design

Sep 15, 2026cs.LG

Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds

Generative modeling of time-dependent data is typically formulated on a discrete temporal grid, restricting supervision to the observed timestamps in the training data. We instead frame generation as continuous-time evolution on a learned data manifold. To this end, we leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths. Because these dynamics follow transitions that respect the geometry learned by the score model, they support generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data. Moreover, this geometric formulation allows us to train the vector field simulation-free through a regression objective. To improve long-horizon rollout robustness, we introduce an objective that promotes path-relative transverse exponential stability. While motivated by stability theory, it admits a practical interpretation as denoising score matching transverse to the interpolation path. Further, we extend the framework to a probabilistic setting that models a distribution over plausible future trajectories. We demonstrate the method on natural video and scientific dynamical data, including temporal super-resolution, PDE-based spatiotemporal fields, and molecular dynamics. Our results show that score-based priors provide a strong foundation for learning stochastic continuous-time generative dynamics.

Jan Tauberschmidt, Brian B. Moser, Stanislav Frolov +3

DFKI Kaiserslautern · RPTU Kaiserslautern · Imperial College London

Dynamical Systems Latent Dynamics Modeling Generative Modeling Score-Based Generative Modeling

Sep 15, 2026cs.AI

From Manual Construction to AI-Driven Scenario Emergence: Rethinking Catastrophe Risk Modeling

Traditional catastrophe (CAT) risk models rely on costly manual construction to generate extreme weather scenarios, an approach largely unchanged since the 1990s. As climate extremes intensify, this creates mounting challenges to the entire risk transfer chain. This study proposes the TAISE framework, which repurposes AI weather forecasting models to produce coherent extreme weather sequences at a fraction of traditional costs. Through self-iterative generation, the framework produces continuous global atmospheric fields from which extreme events emerge. A proof-of-concept experiment demonstrates an order-of-magnitude reduction in computational cost compared with conventional methods, while capturing temporal continuity and cross-regional correlations absent in snapshot-based approaches. These findings suggest a pathway toward democratising catastrophe risk quantification and enabling dynamic, comprehensive portfolio assessment for insurers, reinsurers, ILS fund managers and public-sector risk managers.

Hang Gao

Generative Modeling

Sep 14, 2026cs.LG

Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration

Drifting models offer a promising route to faster generative AI: they perform gradual transport during training, while generating new samples in a single step. This paper asks whether the underlying drifting process can converge rapidly to a target distribution under ideal conditions, before finite-data or optimization effects are introduced. We show that its convergence rate depends critically on how it handles spatial scale. With a single fixed resolution, fine-scale features of the target can become nearly invisible, leading to extremely slow convergence. We introduce a multihead approach that combines scale-normalized information across a continuum of resolutions. We prove that this multihead approach restores exponential convergence near standard reference distributions. These results identify fixed resolution as a key bottleneck and provide a simple route to faster one-step generative models.

Arthur Stéphanovitch, Eddie Aamari

Centre de recherche en économie et statistique · ENSAE, IP Paris · Département de Mathématiques et Applications +1

One-Step Generative Modeling Generative Modeling Drifting Models

Sep 14, 2026cs.LG

Branched Optimal Transport Amortization

Methods of Branched Optimal Transport (BOT) mimic the economy and efficiency of natural tree-like structures, such as those found in rivers and biological systems. These methods are widely applicable for designing efficient networks in society, from river basins and blood vessels to mail and gas distribution systems. However, they remain understudied in the context of designing deep generative models, particularly at a large scale. Standard continuous-time generative models, such as the flow matching approach, fail to capture the inherent hierarchical and branching patterns present in real-world data. Current models provide no mechanism for flows to merge or share pathways to minimize total transport cost. Inspired by the "economy of scale" principle in BOT, we introduce a novel, scalable branched flow-matching algorithm designed to solve the branched optimal transport problem in high dimensions. Our method adapts the Benamou-Brenier continuous-time optimal transport formulation to learn branched generative flows. These flows allow probability mass to aggregate along common pathways before branching out to diverse targets. Parametrized by neural networks, our method effectively learns complex branched generative processes. We demonstrate its effectiveness on challenging high-dimensional tasks in biology and image generation.

Semyon Semenov, Viktor Kovalchuk, Meir Roketlishvili +4

MBZUAI

Flow Matching Generative Modeling Flow-Based Generative Modeling Optimal Transport

Sep 14, 2026physics.ins-det

Fast BIB simulation at a future Muon Collider with generative machine learning

Beam-induced background (BIB) from muon decay products will be an overwhelming and unavoidable background at a future Muon Collider. In order to develop robust event reconstruction algorithms, we need large amounts of accurate BIB simulation to test on. BIB simulation is currently compute-limited: the simulated sample presently used for BIB overlay, which statistically represents approximately

10\%

of a single unique event's worth of simulated BIB, requires on the order of

10^6

HS23

\cdot

hours to generate and occupies approximately

100

GB on disk. In this work, we develop the first machine learning models for fast BIB generation in tracking detectors. We consider two classes of architectures: a slower but higher-fidelity tabular diffusion model, and a faster but lower fidelity circular spline flow model. We find that both classes of architectures produce BIB hits and tracks that closely resemble those of available full simulation hits and tracks, and that the machine learning models can produce BIB in over an order of magnitude less time than what is needed to produce full simulation BIB. We release the model weights with the paper so that the Muon Collider community can use these fast BIB hits for future R&D.

Radha Mastandrea, Shiyu Peng, Benjamin Rosser +1

Enrico Fermi Institute, The University of Chicago, Chicago, IL 60637, USA · Data Science Institute, The University of Chicago, Chicago, IL 60637, USA · Department of Physics, Brown University, Providence, RI 02912, USA +1

Tabular Diffusion Models Generative Modeling High-Energy Physics Physics-Based Simulation

Sep 12, 2026cs.LG

CyFM: Cylindrical Optimal Transport for Few-Step Complex-Valued Flow Matching

Complex-valued signals like MRI and audio spectrograms are typically modelled as flat two-channel Euclidean data. The inherited Euclidean metric

dA^2 + A^2 dθ^2

vanishes at the origin, leaving phase unpenalised exactly where the signal is weakest. We replace it with the decoupled product metric

dA^2 + dθ^2

on the cylindrical closure

[0, \infty) \times S^1

, which stays non-degenerate at

A = 0

. We measure what this substitution costs and buys. Exact analytical bridges across synthetic fields, fastMRI knee data, and LibriSpeech spectrograms show Cartesian paths induce a heavy-tailed angular velocity distribution (Pareto index

\approx 1

). Under independent coupling, 43%-49% of signal energy falls on paths turning faster than

π

rad per unit time. Cylindrical paths never reach this speed. We formulate Cylindrical Flow Matching (CyFM) to strictly bound the angular regression target, coupling noise and data via exact minibatch Optimal Transport jointly over whole fields. This coupling reduces few-step generation error by 3%-60%. CyFM achieves lower generative error than the best Cartesian baseline at every step up to

k = 8

on synthetic fields and speech spectrograms, with all seeds separated. On knee MRI, the single-step advantage is 1.8x. At convergence (

k = 100

), the two geometries show no significant difference. Finally, a prior-only control exposes the cost of flat parametrisation: on synthetic fields, a single Cartesian Euler step performs worse than the unintegrated noise prior (0.376 vs. 0.150).

Marcel Musiałek, Iga Wolanin, Damian Ryczko +2

Wrocław University of Science and Technology Wrocław, Poland

Flow Matching One-Step Generative Modeling Generative Modeling Flow-Based Generative Modeling Optimal Transport

Sep 11, 2026cs.LG

Particle GFlowNets: Rethinking Generative Marginalization Models

Generative Marginalization Models (MaMs) have been recently introduced as efficient neural sampling models for any-order autoregressive modelling of discrete distributions. By learning both the marginal and conditional probabilities of a persistent-block Gibbs sampler, MaMs enable fast posterior evaluation with a single neural network forward pass. While prior work has considered MaMs to be distinct from Generative Flow Networks (GFlowNets), a well-established paradigm for inference in discrete stochastic models, we show that they are equivalent. Then, we also extend MaMs' sampling strategy to non-autoregressive generative processes. In particular, we describe an automatic criterion for full-state rejuvenation of the Gibbs sampler, derived from the Gelman-Rubin statistic, which plays a key role in speeding up learning convergence. Our experiments show that our method, called Particle GFlowNets, markedly accelerates training in large combinatorial spaces.

Tiago da Silva, Diego Mesquita, Salem Lahlou

MBZUAI · School of Applied Mathematics, Getulio Vargas Foundation

Markov Chain Monte Carlo Generative Flow Networks Generative Modeling Flow-Based Generative Modeling

Sep 3, 2026cs.LG

SimpleDesign: A Joint Model for Protein Sequence and Structure Codesign

Proteins are fundamental to biological processes, with their function determined by the complex interplay between the amino acid sequence and the three-dimensional structure. Developing generative models capable of understanding this intrinsically multi-modal relationship is crucial for fields like drug discovery and protein engineering. Existing models often rely on a multi-stage training process where autoencoders that tokenize data into latent representations are trained in a first stage. Secondly, a generative model is trained on the latent representation of the autoencoder(s), i.e., generative modeling in a latent space. We hypothesize that this multi-stage training is not necessary to obtain performant co-design models and thus present SimpleDesign, an effective multi-modal protein design model trained directly in the data space. SimpleDesign leverages a single-stage end-to-end objective that combines discrete cross-entropy for sequences and a regression objective for structures. In order to effectively model the difference in sequence and structure modalities, we develop a Mixture-of-Transformer architecture that allows modality-specific processing while keeping global self-attention over both modalities. We train SimpleDesign on over 2M sequence-structure pairs achieving strong performance across co-design and unconditional sequence/structure generation benchmarks.

Jiarui Lu, Yuyang Wang, Yizhe Zhang +4

Mila, Université de Montréal, Apple · Apple

Unified Multimodal Models Generative Modeling Multimodal Generation Molecular Generation Protein Design

Sep 2, 2026cs.CV

Thinking in Pictures: A Systematic Benchmark for Reasoning-driven Image Generation

Recent advancements in unified generative models (UGMs) and world simulators have achieved unprecedented results in visual perception and synthesis. However, these models primarily rely on surface-level event alignment, leaving the capacity for high-level visual reasoning underexplored. True visual generative intelligence demands "Reasoning-to-Generation", an ability to infer latent rules from visual inputs and manifest solutions through precise, logically constrained visual outcomes. We introduce RIG-BENCH, a novel comprehensive benchmark that systematically evaluates Reasoning-driven Image Generation (RIG) across four cognitively demanding domains: Concept-based, Transformation-based, Pattern & Structure, and Scenario-based. Featuring 2000 curated samples, RIG-BENCH serves as a rigorous stress test for RIG. Our extensive evaluations of state-of-the-art UGMs and image/video generation models reveal a significant reasoning-generation gap, wherein models frequently produce locally plausible but globally illogical outputs. RIG-BENCH provides a vital diagnostic framework to guide the development of next-generation, logically grounded UGMs and world simulators.

Yutong Liu, Nan Huang, Xu Cao +1

University of Illinois Urbana-Champaign · New York University

Image Generation Image Generation Evaluation Visual Reasoning Generative Modeling

Sep 2, 2026stat.ML

Full-Model Optimality for Tunable Linear Generative Priors in Compressed Sensing

Generative models have been studied experimentally and theoretically as priors for inverse problems such as compressed sensing. Recent work by Gunn et al. studied the use of generative priors with tunable complexity, where a family of generative priors with varying complexity is maintained and a specific complexity can be selected at inversion time. They demonstrated that lower reconstruction errors can be experimentally attained for a variety of inverse problems by appropriately tuning the complexity of the generative prior. In the present paper, we establish theory for compressed sensing in the setting of a tunable family of linear generative priors naturally related through their singular value decompositions. We prove that in noiseless Gaussian compressed sensing, the full-dimensional linear prior attains the minimum expected reconstruction error over the entire family of linear priors. Thus, in this idealized linear noiseless setting, tuning to a lower-complexity prior does not improve the expected reconstruction error. This result is in contract to the behavior of denoising, where lower complexity priors attain lower reconstruction errors due to a standard bias-variance tradeoff. This result indicates that the experimental benefits of tunability in compressed sensing with neural network priors arises due to nonlinearities in the generative models.

Zhaoming Li, Paul Hand

Department of Mathematics, Northeastern University, Boston, MA 02115, USA. · Department of Mathematics and Khoury College of Computer Sciences, Northeastern University, Boston, MA 02115, USA.

Compressed Sensing Model Selection Generative Modeling

Sep 2, 2026cs.CL

Do Large Language Models Capture the Diversity in their Training Data?

Large language models are trained to model conditional distributions over text, yet it remains inadequately understood whether they capture the full diversity of plausible outputs present in their training data. We study this question through an information-theoretic lens by comparing the conditional entropy of model-generated outputs with that of the corresponding training data. Given paired input-output samples, we use conditional entropy and its matrix-based analogue based on von Neumann entropy to measure output variability beyond what is explained by the conditioning input, without requiring multiple reference outputs for the same prompt. Across LLM families with publicly available training data, including OLMo, Pythia, and GPT-Neo, we consistently find that model-generated outputs exhibit lower conditional entropy than their training data, across different model scales, sequence lengths, and decoding strategies. We observe a similar conditional diversity gap beyond language modeling, including class-conditioned ImageNet generators and text-conditioned models trained on MS-COCO. To address this gap, we propose a post-hoc correction mechanism that generates multiple outputs for each input and reweights them through a matrix-entropy projection, increasing conditional diversity while remaining close to the original model distribution. We prove the concavity of the matrix-based conditional entropy functional, which makes the resulting entropy-constrained projection a convex optimization problem, and develop a scalable mirror-descent algorithm for its implementation. Our results reveal a systematic conditional diversity gap between modern generative models and their training data, and provide an information-theoretic framework for measuring and mitigating this gap.

Youqi Wu, Farzan Farnia

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

Generative Modeling

Sep 2, 2026stat.ML

Schrödinger Bridges on Lie Group Manifolds for Probabilistic Intrinsic Generation

Generative modeling directly on geometric manifolds can avoid errors introduced by flattening non-Euclidean data, repeated ambient projection, and coordinate inconsistency in Euclidean representations. Schrodinger bridges provide a probabilistic generative framework for entropy-regularized transport between prescribed endpoint distributions. We study Schrodinger bridges for kinetic dynamics on Lie group manifolds with state X_t = (g_t, xi_t) in G x g, allowing endpoint observations to constrain only the variables that are actually measured. In particular, the entropy projection determines the conditional law of the unobserved endpoint velocities. For the same observed endpoint bridge, we develop two computational realizations: Wrapped-Kernel Bridge Calibration (WKBC) uses an explicit periodized kinetic kernel on compact Abelian groups, whereas Reciprocal Conditional-Control Bridge Matching (RCCBM) handles compact non-Abelian groups through two-sided endpoint calibration and mollified conditional-control matching. The canonical teacher-mixture path law is itself a Markov reciprocal law, so forward generation uses a calibrated initial law and one learned Doob controller. Moreover, we establish a modular error bound in the bounded-Lipschitz path metric that provides a clean separation of errors due to endpoints, control regression, initialization, discretization, and related approximations. Experiments on multiple Lie group manifold datasets validate the feasibility and consistency of our proposed method, covering protein and RNA torsions, SO(3), U(n), and the Protein Conformational Transition Pathway Generation task using mdCATH trajectories in a compact reduced representation. The source code is publicly available at https://github.com/cafferyzhang12/Schr-dinger_Bridge_on_LieGroup.

Shizhe Zhang, Mingyang Zhao, Lei Ma

1National Biomedical Imaging Center, College of Future Technology, Peking University, Beijing, China · 2State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Schrödinger Bridges Generative Modeling Lie Group Methods Molecular Generation

Sep 1, 2026cs.SI

A Network Science Perspective on Evaluating Deep Graph Generative Models

Traditional network models from network science, such as the Erdos-Renyi and configuration models, generate random networks that reproduce few selected topological properties observed in real-world networks. Deep graph generative models emerge as a data-driven approach, leveraging deep neural network architectures to learn complex structural distributions directly from real-world networks to generate more realistic synthetic networks. Because real social contact networks cannot be shared due to privacy risks, synthetic networks serve as an alternative for developing and evaluating epidemic mitigation strategies. In this work, we evaluate deep graph generative models as well as the configuration from a network science perspective by assessing both the topological similarity between generated and real-world networks and their utility in identifying effective node immunization strategies to sup- press epidemic/misinformation spreading. It is found that two deep graph generative models produce synthetic networks that closely resemble the structural properties of real-world networks, enabling them to identify effective immunization strategies.

Tianrui Mao, Abele Malan, Megha Khosla +2

Delft University of Technology, the Netherlands · University of Neuchâtel, Switzerland

Synthetic Data Generation Generative Modeling Synthetic Data Evaluation

Aug 31, 2026cs.CV

Motion-Saliency Complementary Masked Modeling for Point Cloud Video Understanding

Point cloud video representation learning is crucial for 3D dynamic scene understanding. In this paper, we propose MoSaiC, a novel Motion-Saliency Complementary masked modeling framework for self-supervised point cloud video representation learning. MoSaiC couples three components: Curriculum Motion-Saliency Masking (CMSM), which guides the masking process toward motion-salient tokens under a curriculum schedule; Normal-Flow Motion (NFM) modeling, which supervises the local rigid rotation of each token in the Lie algebra so(3) as an explicit geometric motion target; and Cross-view Token Consistency Prediction (CTCP), which enforces consistency between two complementary masked views at the token level. Together, these components allow MoSaiC to effectively capture both appearance and motion dynamics. Extensive experiments on multiple downstream tasks, including action recognition, temporal action segmentation, and point-level semantic segmentation, demonstrate the effectiveness of our approach.

Wei Wang, Yiding Sun, Yuyan Wang +4

School of Computer Science and Technology, Xi’an Jiaotong University, Xi’an, 710049, China · Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen, 518107, China · School of Software Engineering, Xi’an Jiaotong University, Xi’an, 710049, China +4

Point Cloud Learning Generative Modeling Motion Representation Learning Self-Supervised Visual Representation Learning

Aug 13, 2026cs.LG

Novel Knowledge-Guided Generative Methods for Synthetic Transcriptomic Data

As biomedical research increasingly relies on data-intensive tools, the quality and utility of datasets are critical. Challenges such as imbalances, biases, and ethical or legal constraints often limit access to high-quality data. Synthetic data generation can help overcome these limitations. Here, we present a comparative analysis of generative models for transcriptomic data, investigating strategies to incorporate prior biological knowledge via gene graphs. This ensures that synthetic data capture real-world gene patterns, maintaining their usefulness for downstream tasks. In particular, we introduce and benchmark three variants of the Generative Adversarial Network. Among the alternatives, MK-TGAN - an innovative multi-kernel, Graph Neural Network-based model - stands out for its performance in terms of both the realism and utility of the generated data. Unlike other methods, MK-TGAN leverages prior knowledge graphs by exploiting graph neural networks. Our results show that prior knowledge integration strategies improve performance, and that MK-TGAN consistently produces synthetic samples with superior realism and biological plausibility.

Francesca Pia Panaccione, Sofia Mongardi, Marco Masseroli +1

DEIB - Dipartimento Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy

Graph Neural Networks Synthetic Data Generation Generative Modeling Genomics Generative Adversarial Networks

Aug 13, 2026cs.CV

GeoCache: Training-Free Acceleration of Multi-View Texture Diffusion via Geometric Delta Transport

Geometry-conditioned multi-view diffusion enables high-quality 3D texture generation, but its repeated per-view denoiser evaluations introduce substantial computational cost. Existing training-free accelerators primarily exploit temporal redundancy by reusing computation across denoising steps. In multi-view texturing, however, skipping a step also removes the cross-view interaction that continually aligns different observations of the same surface, leading to rapidly degraded consistency and fidelity. Our analysis identifies a complementary source of redundancy: although intermediate features remain view-specific, geometrically corresponding surface points exhibit transferable evolution in their predicted clean signals. Based on this observation, we introduce \gc{}, a training-free plugin that evaluates a rotating subset of anchor views and transports their geometry-aligned per-step

\xz

updates to the remaining views. Periodic full-view computation controls accumulated error, while sampler-consistent reconstruction preserves the denoising trajectory. \gc{} requires neither retraining nor architectural modification and uses the position maps already available in geometry-conditioned texturing pipelines. Across Hunyuan3D-2.1, SyncMVD, and MVPainter, \gc{} achieves a stronger speed--fidelity trade-off than temporal caches and step reduction at operating points above

2\times

. On Hunyuan3D-2.1, it delivers a

2.21\times

denoiser-loop speedup with an MV-LPIPS of 0.0293 and an MV-PSNR of 33.60 dB, providing the best fidelity among all tested methods above

2\times

. The same transferred configuration reaches the highest speedup and lowest FLOPs on SyncMVD, while \gc{} achieves the lowest FLOPs and best fidelity among the accelerated methods on MVPainter. These results establish cross-view geometry as an effective acceleration axis for multi-view texture diffusion.

Haotang Li, Zhenyu Qi, Shaohan Henry Wang +6

Department of Eletrical and Computer Engineering, University of Arizona, Tucson, AZ · Department of Computer Science, East Carolina University, Greenville, NC · Department of Computer Engineering and Computer Science,California State University, Long Beach, CA +1

Multi-View Consistency Generative Modeling Diffusion Model Inference Acceleration Texture Synthesis