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

May 7, 2026cs.LG

A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models, score-based generative models, and flow matching are instances of learning a time-dependent vector field that induces a family of marginals

(ρ_t)_{t \in [0,1]}

governed by continuity and Fokker-Planck equations. Such a unified theory is timely because these methods are converging methodologically, yet fragmented notation and competing derivations continue to obscure their shared structure and the practical tradeoffs governing sampling, stability, and computation. Within this framework, we (i) derive reverse-time sampling for diffusion and score-based models as controlled stochastic dynamics, (ii) show that the probability flow ODE yields identical marginals and connects diffusion to likelihood-based normalizing flows, and (iii) interpret flow matching as direct regression of the velocity field under a chosen interpolation, clarifying when it coincides with or differs from score-based training. We compare objectives, sampling schemes, and discretization errors under unified notation, discuss connections to Schrodinger bridges and entropic optimal transport, and summarize theoretical guarantees and open problems on approximation, stability, and scalability.

Aditya Ranganath, Mukesh Singhal

Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore, CA 94551, USA · Department of Electrical Engineering University of California Merced, CA 95343, USA

Flow Matching Generative Modeling Flow-Based Generative Modeling Score-Based Generative Modeling Diffusion Models

May 7, 2026cs.LG

BRICKS: Compositional Neural Markov Kernels for Zero-Shot Radiation-Matter Simulation

We introduce a new strategy for compositional neural surrogates for radiation-matter interactions, a key task spanning domains from particle physics through nuclear and space engineering to medical physics. Exploiting the locality and the Markov nature of particle interactions, we create a \emph{next-particle prediction} kernel using hybrid discrete-continuous transformer models based on Riemannian Flow Matching on product manifolds. The model generates variable-sized typed sets of particles and radiation side effects that are the result of the interaction of an incident particle with a material volume. The resulting kernel can be composed to simulate unseen large-scale material distributions in a zero-shot manner. Unlike mechanistic simulators, our model is designed to be differentiable, provides tractable likelihoods for future downstream applications. A significant computational speed-up on GPU compared to CPU-bound mechanistic simulation is observed for single-kernel execution. We evaluate the model at the kernel level and demonstrate predictive stability over multi-round autoregressive rollouts. We additionally release a novel 20M-event radiation-matter interaction dataset for further research.

Richard Hildebrandt, Evangelos Kourlitis, Baran Hashemi +7

Technical University of Munich · Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany · SLAC National Accelerator Laboratory +3

Neural Surrogate Modeling Riemannian Flow Matching Generative Modeling Physics-Based Simulation

May 7, 2026cs.LG

SymDrift: One-Shot Generative Modeling under Symmetries

Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such as rotations in three-dimensional space. Equivariant diffusion and flow matching models can incorporate such invariances effectively, even when trained on a non-invariant empirical distribution, but they typically rely on costly multi-step sampling. Recently, drifting models have emerged as an efficient alternative, enabling single-step generation and achieving state-of-the-art performance in generative modeling tasks. However, we show that drifting models face a symmetry-specific challenge, since an equivariant generator does not generally produce the same drifting field as the one obtained from the symmetrized target distribution. Addressing this issue would require expensive symmetrization of the empirical distribution. To avoid this cost, we propose SymDrift, a framework that makes the drifting field itself symmetry-aware. We introduce two complementary strategies: (i) a symmetrized drift in coordinate space based on optimal alignment, and (ii) a

G

-invariant embedding that removes symmetry ambiguity by construction. Empirically, SymDrift outperforms existing one-shot methods on standard benchmarks for conformer and transition state generation, while remaining competitive with significantly more expensive multi-step approaches. By enabling one-shot inference, SymDrift reduces computational overhead by up to 40

\times

compared to existing baselines, making it promising for high-throughput applications such as virtual drug screening and large-scale reaction network exploration.

Samir Darouich, Vinh Tong, Lluís Pastor-Pérez +3

Institute of Artificial Intelligence Institute of Theoretical Chemistry University of Stuttgart

One-Step Generative Modeling Generative Modeling Drifting Models

May 7, 2026stat.ML

Spherical Flows for Sampling Categorical Data

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere

\mathbb S^{d-1}

. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on

\mathbb S^{d-1}

to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on

(\mathbb S^{d-1})^L

both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.

Jannis Chemseddine, Gregor Kornhardt, Gabriele Steidl

Technische Universität Berlin

Flow Matching Synthetic Data Generation Generative Modeling Flow-Based Generative Modeling Sequence Modeling

May 6, 2026cs.LG

On the Wasserstein Gradient Flow Interpretation of Drifting Models

Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest descent for a functional in the space of probability measures, equipped with the geometry of optimal transport. Unlike previous WGF-based contributions, GMD can be thought of as directly targeting a fixed point of a specific WGF flow. We demonstrate three main results: first, that one algorithm proposed by Deng et al. (2026) corresponds to finding the limiting point of a WGF on the KL divergence, with Parzen smoothing on the densities. Second, that the algorithm actually implemented by Deng et al. (2026) corresponds to a different procedure, which bears some resemblance to the fixed point of a WGF on the Sinkhorn divergence, but lacks certain desirable properties of the latter. Third, the same same idea can be extended to the limiting point of other WGFs, including the Maximum Mean Discrepancy (MMD), the sliced Wasserstein distance, and GAN critic functions.

Arthur Gretton, Li Kevin Wenliang, Alexandre Galashov +3

Google DeepMind

Wasserstein Gradient Flows Generative Modeling Drifting Models Wasserstein Distance

May 5, 2026cs.AI

Self-Improvement for Fast, High-Quality Plan Generation

Generative models trained on synthetic plan data are a promising approach to generalized planning. Recent work has focused on finding any valid plan, rather than a high-quality solution. We address the challenge of producing high-quality plans, a computationally hard problem, in sub-exponential time. First, we demonstrate that, given optimal data, a decoder-only transformer can generate high-quality plans for unseen problem instances. Second, we show how to self-improve an initial model trained on sub-optimal data. Each round of self-improvement combines multiple model calls with graph search to generate improved plans, used for model fine-tuning. An experimental study on four domains: Blocksworld, Logistics, Labyrinth, and Sokoban, shows on average a 30% reduction in plan length over the source symbolic planner, with over 80% of plans being optimal, where the optimum is known. Plan quality is further improved by inference-time search. The model's latency scales sub-exponentially in contrast to the satisficing and optimal symbolic planners to which we compare. Together, these results suggest that self-improvement with generative models offers a scalable approach for high-quality plan generation.

Robert Gieselmann, Henrike von Huelsen, Mihai Samson +9

Amazon

Symbolic Planning Generative Modeling

May 5, 2026cs.LG

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.

Hao Zhou, Rui Zhang, Han Wan +1

Gaoling School of Artificial Intelligence, Renmin University of China

Physics-Informed Generative Modeling Uncertainty Quantification Rectified Flow Generative Modeling Physics-Informed ML Flow-Based Generative Modeling+1

May 5, 2026q-bio.QM

A-CODE: Fully Atomic Protein Co-Design with Unified Multimodal Diffusion

We present A-CODE, a fully atomic unified one-stage protein co-design model that simultaneously refines discrete atom types and continuous atom coordinates. Unlike predominant two-stage methods that cascade structure design with amino acid-level sequence design, our approach is fully atomic within a unified multimodal diffusion framework, in which residue identities are inferred solely from atom-level predictions. Built upon the powerful all-atom architecture, A-CODE achieves superior designability for unconditional protein generation, outperforming all existing one-stage and two-stage design models. For binder design, A-CODE rivals and even outperforms existing state-of-the-art two-stage design models and, compared with the existing one-stage co-design model, achieves a drastic tenfold improvement in success rate on hard tasks. The inherent flexibility of our atomic formulation enables, for the first time, seamless adaptation to non-canonical amino acid (ncAA) modeling. Our fully atomic framework establishes a new, versatile foundation for all-atom generative modeling that can be naturally extended to complex biomolecular systems.

Chaoran Cheng, Jiaqi Guan, Milong Ren +5

University of Illinois Urbana-Champaign · 2ByteDance Seed

Generative Modeling Molecular Generation Protein Design Protein Binder Design Multimodal Diffusion Models

May 4, 2026cs.AI

Fine-Grained Graph Generation through Latent Mixture Scheduling

Structure aware graph generation aims to generate graphs that satisfy given topological properties. It has applications in domains such as drug discovery, social network modeling, and knowledge graph construction. Unlike existing methods that only provide coarse control over graph properties, we introduce a novel conditional variational autoencoder for fine-grained structural control in graph generation. The approach refines the decoder's latent space by dynamically aligning graph- and property-driven representations to improve both graph fidelity and control satisfaction. Specifically, the approach implements a mixture scheduler that progressively integrates graph and control priors. Experiments on five real-world datasets show the efficacy of the proposed model compared to recent baselines, achieving high generation quality while maintaining high controllability.

Nidhi Vakil, Hadi Amiri

Department of Computer Science University of Massachusetts Lowell

Graph Generation Generative Modeling Conditional Variational Autoencoder Conditional Generative Modeling

May 4, 2026cs.GR

Generative Modeling with Orbit-Space Particle Flow Matching

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Sinan Wang, Jinjin He, Shenyifan Lu +3

Georgia Institute of Technology, USA

Flow Matching One-Step Generative Modeling Generative Modeling 3D Shape Generation Permutation-Invariant Learning Flow-Based Generative Modeling

May 3, 2026cs.AI

Runtime Evaluation of Procedural Content Generation in an Endless Runner Game Using Autonomous Agents

Procedural Content Generation (PCG) enables game content to be created algorithmically without direct manual level-design effort, but it introduces a serious evaluation problem: generated content may become unbalanced, blocked, repetitive, or technically unsolvable. This paper presents Momentum, an endless-runner game that integrates runtime terrain generation, environment object spawning, and autonomous agent-based evaluation into a single gameplay loop. Ground tiles and environmental objects are generated dynamically as the player advances, object placement follows a constraint-driven mechanism inspired by Wave Function Collapse (WFC), and the runtime navigation surface is rebuilt asynchronously to remain consistent with the streamed environment. Two autonomous evaluation agents move ahead of the player and inspect the generated path: an aerial scanner that examines the corridor geometrically, and a ground-traversal agent that validates the same region from a navigational perspective. The evaluation pipeline combines ray casting, volumetric physics sweeps, obstacle-layer filtering, and structured crash reporting to identify problematic generated scenarios before they reach the player. The work demonstrates how generation and validation can be unified within the same runtime loop, rather than treating evaluation as a separate offline pass. Around this implementation, the paper formulates a measurable evaluation framework along the canonical PCG axes of playability, diversity, controllability, and runtime performance, derives a structural saturation bound on the spawner from its own placement constraints, and quantifies the per-segment scanning cost of the agents from first principles.

Rishabh Kar

Department of Informatics King’s College London London, United Kingdom

Generative Modeling Procedural Content Generation Automated Evaluation

May 3, 2026stat.ML

Missingness-aware Data Imputation via AI-powered Bayesian Generative Modeling

Missing data imputation remains a fundamental challenge in modern data science, especially when uncertainty quantification is essential. In this work, we propose MissBGM, an AI-powered missing data imputation method via Bayesian generative modeling that bridges the expressive flexibility of neural networks with the statistical rigor of Bayesian inference. Unlike existing methods that often focus on point estimates or treat the missingness mechanism implicitly, MissBGM explicitly and jointly models the data-generating and missingness mechanisms, providing principled posterior uncertainty over imputations rather than a single point estimate. We develop a stochastic optimization framework with alternating updates among missing values, model parameters, and latent variables until convergence. Our theoretical analysis shows that estimates of missing values from MissBGM converge consistently under mild assumptions. Empirically, we demonstrate that MissBGM achieves superior performance over traditional imputers and recent neural network-based methods across extensive experimental settings. These results establish MissBGM as a principled and scalable solution for modern missing data imputation. The code for MissBGM is open sourced at https://github.com/liuq-lab/MissBGM.

Qiao Liu

Department of Biostatistics Yale University

Incomplete Data Imputation Uncertainty Quantification Learning with Missing Data Generative Modeling

May 2, 2026cs.LG

Barriers to Counterfactual Credit Attribution for Autoregressive Models

Generative AI disrupts the practice of giving credit to work that came before. Ideally, a generative model would give credit to any work on which its output depends in a significant way. \emph{Counterfactual credit attribution} (CCA) is a technical condition formalizing this goal--a relaxation of differential privacy--recently introduced by Livni, Moran, Nissim, and Pabbaraju [2024] who studied it in the PAC learning setting. We initiate the study of CCA generative models. Specifically, we consider autoregressive models giving credit to a deployment-time dataset (e.g., a RAG database). We uncover barriers to two natural approaches to CCA autoregressive models. First, we show that imposing CCA on the underlying next-token predictor does not guarantee that the model is CCA: CCA does not compose autoregressively (unlike DP). Second, we consider a different approach to building CCA models which we call \emph{retrofitting}. Retrofitting takes a model that does not attribute credit, and adds credit onto it. We prove a lower bound for CCA retrofitting under a weak optimality requirement. Given black-box access to the starting model, retrofitting requires query complexity exponential in the length of the model's outputs.

Aloni Cohen, Chenhao Zhang

Generative Modeling Counterfactual Credit Assignment Autoregressive Modeling

May 1, 2026cs.LG

Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems

Complex physical systems, from supersonic turbulence to the macroscopic structure of the universe, are governed by continuous multiscale dynamics. While modern machine learning architectures excel at mapping the high-dimensional observables of these systems, it remains unclear whether they internalize the governing physical laws or merely interpolate discrete statistical correlations. Standard Explainable AI (XAI) architectures, particularly perturbation-based and gradient-saliency methods, rely on pixel-wise perturbations, which generate unphysical artifacts and push inputs off the valid empirical distribution. To resolve this, we introduce a diagnostic framework driven by Constrained Diffusion Decomposition (CDD), a diffusion-based multiscale data decomposition algorithm that enables physically constrained data generation and model evaluation via scale-aware modifications. Applying this framework to a Denoising Diffusion Probabilistic Model (DDPM), we execute deterministic interventions directly within the continuous, CDD-based scale space. We demonstrate that under moderate physical perturbations, the unconstrained generative model exhibits localized structural freezing and non-linear instability rather than continuous PDE-like responses. The network fails to maintain cross-scale continuity, causing the generative trajectory to diverge when pushed into unseen physical states. By synthesizing a continuum of physically coherent states, this scale-informed methodology establishes a controlled test ground to evaluate algorithmic vulnerabilities, providing the rigorous physical constraints necessary for future architectures to respect the multiscale causality of the natural universe.

Mengke Zhao, Guang-Xing Li, Duo Xu +1

School of Astronomy and Space Science, Nanjing University, 163 Xianlin Avenue, Nanjing 210023, Jiangsu, People’s Republic of China · Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210023, Jiangsu, People’s Republic of China · South-Western Institute for Astronomy Research, Yunnan University, Kunming 650091, People’s Republic of China +1

Generative Modeling Generative AI Evaluation Diffusion Models Physical Adversarial Attacks

May 1, 2026cs.LG

Proteo-R1: Reasoning Foundation Models for De Novo Protein Design

Deep learning in \emph{de novo} protein design has achieved atomic-level fidelity. However, existing models remain largely non-deliberative: they directly synthesize molecular geometries without explicitly reasoning about which residues or interactions are functionally essential. As a result, design decisions are entangled with continuous sampling dynamics, limiting interpretability, controllability, and systematic reuse of biochemical knowledge. We introduce \textbf{Proteo-R1}, a reasoning-guided protein design framework that explicitly decouples \emph{molecular understanding} from \emph{geometric generation}. Proteo-R1 adopts a dual-expert architecture in which a multimodal large language model (MLLM) serves as an \emph{understanding expert}, analyzing protein sequences, structures, and textual context to identify key functional residues that govern binding and specificity. These residue-level decisions are then passed as hard constraints to a separate diffusion-based \emph{generation expert}, which performs conditional co-design while respecting the fixed interaction anchors. This factorization mirrors how human experts approach molecular engineering: first, reasoning about critical interactions, then optimizing geometry subject to those constraints. By operationalizing reasoning as explicit residue-level commitments rather than latent textual guidance, Proteo-R1 achieves stable, interpretable, and modular integration of LLM reasoning with state-of-the-art geometric generative models. Code, data, and demos are available at https://smiles724.github.io/r1/.

Fang Wu, Weihao Xuan, Heli Qi +26

Stanford University

Generative Modeling 3D Molecular Generation Molecular Generation Protein Design Large Language Model-Guided Scientific Discovery Conditional Generative Modeling

Apr 30, 2026cs.CV

When Do Diffusion Models learn to Generate Multiple Objects?

Text-to-image diffusion models achieve impressive visual fidelity, yet they remain unreliable in multi-object generation. Despite extensive empirical evidence of these failures, the underlying causes remain unclear. We begin by asking how much of this limitation arises from the data itself. To disentangle data effects, we consider two regimes across different dataset sizes: (1) concept generalization, where each individual concept is observed during training under potentially imbalanced data distributions, and (2) compositional generalization, where specific combinations of concepts are systematically held out. To study these regimes, we introduce mosaic (Multi-Object Spatial relations, AttrIbution, Counting), a controlled framework for dataset generation. By training diffusion models on mosaic, we find that scene complexity plays a dominant role rather than concept imbalance, and that counting is uniquely difficult to learn in low-data regimes. Moreover, compositional generalization collapses as more concept combinations are held out during training. These findings highlight fundamental limitations of diffusion models and motivate stronger inductive biases and data design for robust multi-object compositional generation.

Yujin Jeong, Arnas Uselis, Iro Laina +2

TU Darmstadt & hessian.AI · University of Tübingen · Visual Geometry Group, University of Oxford +1

T2I Generation Compositional Image Generation Generative Modeling T2I Diffusion Models Compositional Generalization

Apr 30, 2026cs.CV

Visual Generation in the New Era: An Evolution from Atomic Mapping to Agentic World Modeling

Recent visual generation models have made major progress in photorealism, typography, instruction following, and interactive editing, yet they still struggle with spatial reasoning, persistent state, long-horizon consistency, and causal understanding. We argue that the field should move beyond appearance synthesis toward intelligent visual generation: plausible visuals grounded in structure, dynamics, domain knowledge, and causal relations. To frame this shift, we introduce a five-level taxonomy: Atomic Generation, Conditional Generation, In-Context Generation, Agentic Generation, and World-Modeling Generation, progressing from passive renderers to interactive, agentic, world-aware generators. We analyze key technical drivers, including flow matching, unified understanding-and-generation models, improved visual representations, post-training, reward modeling, data curation, synthetic data distillation, and sampling acceleration. We further show that current evaluations often overestimate progress by emphasizing perceptual quality while missing structural, temporal, and causal failures. By combining benchmark review, in-the-wild stress tests, and expert-constrained case studies, this roadmap offers a capability-centered lens for understanding, evaluating, and advancing the next generation of intelligent visual generation systems.

Keming Wu, Zuhao Yang, Kaichen Zhang +24

1Tsinghua University · 12LMMs-Lab · 2Nanyang Technological University +9

World Models Generative Modeling Generative AI Evaluation

Apr 30, 2026cs.AI

From LLM-Driven Trading Card Generation to Procedural Relatedness: A Pokémon Case Study

Since the dawn of Trading Card Games, the genre has grown into a multi-billion-dollar industry engaging millions of analog and digital players worldwide. Popular TCGs rely on regular updates, balance adjustments, and rotating constraints to sustain engagement. Yet, as metagames stabilize, predictable strategies dominate and viable card options diminish, often resulting in repetitive and impaired player experiences. This paper investigates the use of Large Language Models and Image Diffusion Models for Procedural Content Generation of TCG cards, addressing these challenges by enabling a personalized infinity of card designs. Modern generative AI not only enables large-scale content creation but could even introduce procedural relatedness, fostering unique connections between players and their cards. We present a pipeline combining player-centric co-creation, fine-tuned embeddings, local LLMs, and Diffusion Models to generate dynamic, personalized cards while potentially expanding creative range. We evaluated the pipeline in a user study with 49 participants who generated 196 Pokémon card samples. Participants rated aesthetics and representativeness of visuals and mechanics, and provided qualitative feedback. Results show high satisfaction and indicate that most participants successfully realized their own ideas through prompt adjustments. These findings lay groundwork for future content generation systems and alternatives to conventional metagame evolution through procedural relatedness.

Johannes Pfau, Panagiotis Vrettis

Utrecht University · Utrecht, Netherlands

Generative Modeling Procedural Content Generation Conditional Generation Generative AI Evaluation

Apr 30, 2026cs.LG

AMGenC: Generating Charge Balanced Amorphous Materials

Amorphous (disordered) materials are solids that have shown great potential in various domains, including energy storage, thermal management, and advanced materials. Unlike crystalline materials that can be described by unit cells containing a few to hundreds of atoms, amorphous materials require larger simulation cells with at least hundreds to thousands of atoms. To advance the design of amorphous materials with desired properties and facilitate the exploration of their vast design space, generative inverse design has emerged as a promising approach. It aims to directly output materials with properties closely aligned with the desired ones using probabilistic generative models conditioned on desired properties, which can be more resource efficient than the traditional trial-and-error approach. However, due to the inherent stochasticity of probabilistic generative models, when element assignments are unconstrained, a large portion of generated materials may be charge unbalanced, and no existing methods can effectively mitigate this limitation. In this work, we propose AMGenC, a new generative inverse design method for amorphous materials that can guarantee the generation of charge balanced samples, with minimal additional computational overhead and without sacrificing inverse design accuracy. AMGenC achieves this through an element noise that gives the generation process a starting point centered around charge balance, and the combination of a per-step soft projection and a final discrete projection for steering the elements toward exact charge balance throughout the generation. We perform extensive experiments on two amorphous materials datasets. Experimental results provide evidence that AMGenC achieves its design goal.

Yan Lin, Jilin Hu, N. M. Anoop Krishnan +1

Department of Computer Science, Aalborg University, Denmark · School of Data Science and Engineering, East China Normal University, China · Department of Civil Engineering, Indian Institute of Technology Delhi, India +2

Materials Science Generative Modeling Conditional Generative Modeling Inverse Design

Apr 30, 2026cs.LG

ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Gabe Guo, Thanawat Sornwanee, Lutong Hao +3

Stanford University

Autoregressive Diffusion Generative Modeling Autoregressive Video Generation Autoregressive Modeling

Apr 29, 2026cs.LG

How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance

In generative modeling, we often wish to produce samples that maximize a user-specified reward such as aesthetic quality or alignment with human preferences, a problem known as \textit{guidance}. Despite their widespread use, existing guidance methods either require expensive multi-particle, many-step schemes or rely on poorly understood approximations. We reformulate guidance as a \textit{deterministic optimal control problem}, yielding a hierarchy of algorithms that subsumes existing approaches at the coarsest level. We show that the \textit{flow map}, an object of significant recent interest for its role in fast inference, arises naturally in the optimal solution. Based on this observation, we propose \textbf{Flow Map Reward Guidance (FMRG)}: a training-free, \textit{single-trajectory} framework that uses the flow map to both integrate and guide the flow. At text-to-image scale, FMRG matches or surpasses baselines across inverse problems and reward-guided generation with \textbf{as few as 3 NFEs}, giving at least an order-of-magnitude speedup in comparison to prior state of the art. Code is available at https://github.com/jrrhuang/fmrg.

Jerry Y. Huang, Justin Lin, Sheel Shah +2

Carnegie Mellon University

Generative Modeling Flow-Based Generative Modeling Conditional Generative Modeling

Apr 28, 2026cs.CL

From World-Gen to Quest-Line: A Dependency-Driven Prompt Pipeline for Coherent RPG Generation

Large Language Models (LLMs) have shown strong potential for narrative generation, but their use in complex, multi-layered role-playing game (RPG) worlds is still limited by issues of coherence, controllability, and structural consistency. This paper explores a dependency-aware, multi-stage prompt pipeline for procedural RPG content generation that models narrative dependencies through structured intermediate representations. The approach decomposes generation into sequential stages: world building, non-player character creation, player character creation, campaign-level quest planning, and quest expansion. Each stage conditions on structured JSON outputs from previous stages. By enforcing schemas and explicit data flow, the pipeline reduces narrative drift, limits hallucinations, and supports scalable creation of interconnected narrative elements. The system is evaluated qualitatively through human-centered analysis across multiple independent runs. Outputs are assessed using criteria such as structural completeness, internal consistency, narrative coherence, diversity, and actionability. Results show that the pipeline consistently generates logically sound and structurally valid RPG content, without quality degradation as complexity increases. Separating high-level campaign planning from detailed quest expansion improves both global structure and local storytelling. These findings suggest that dependency-aware prompt pipelines with structured intermediate representations are an effective design pattern for LLM-based procedural content generation. This approach may also generalize to other domains requiring sequential reasoning over evolving contextual states.

Dominik Borawski, Marta Szulc, Robert Chudy +2

Gda´nsk University of Technology

LLM Prompting Generative Modeling Procedural Content Generation Structured Output Generation Text Generation

Apr 27, 2026eess.SP

EVT-Based Generative AI for Tail-Aware Channel Estimation

Ultra-reliable and low-latency communication (URLLC) will play a key role in fifth-generation (5G) and beyond networks, enabling mission-critical applications. Meeting the stringent URLLC requirements, characterized by extremely low packet error rates and minimal latency, calls for advanced statistical modeling to accurately capture rare events in wireless channels. Traditional methods, such as those that rely on large datasets and computationally intensive estimation techniques, often fail in real-time scenarios. In this paper, a novel framework is proposed to meet URLLC requirements through a synergistic integration of extreme value theory (EVT) with generative artificial intelligence (AI). EVT is used to model channel tail distributions, providing an accurate characterization of rare events. Concurrently, generative AI enables data augmentation and channel parameter estimation from limited samples. The integration of EVT with generative AI can thus help overcome the limitations of generative models in capturing extreme events during channel characterization. Using an experimental dataset collected from an automotive environment, it is demonstrated that this integration enhances data augmentation for extreme quantiles, while requiring fewer samples than traditional analytical EVT methods and generative baselines in online estimation of channel distribution.

Parmida Valiahdi, Niloofar Mehrnia, Walid Saad +1

∗Department of Electrical and Electronics Engineering, Koc University, Istanbul, Turkey · †Department of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden · ‡Department of Electrical and Computer Engineering, Virginia Tech, Virginia, United States

Synthetic Data Augmentation Wireless Communications Generative Modeling Extreme Value Theory

Apr 27, 2026cs.LG

CoreFlow: Low-Rank Matrix Generative Models

Learning matrix-valued distributions from high-dimensional and possibly incomplete training data is challenging: ambient-space generative modeling is computationally expensive and statistically fragile when the matrix dimension is large but the sample size is limited. We propose CoreFlow, a geometry-preserving low-rank flow model that learns shared row/column subspaces across the matrix distribution, and then trains a continuous normalizing flow only on the induced low-dimensional core. CoreFlow is designed for settings where shared low-rank matrix geometry is present, especially in high-dimensional limited-sample regimes. This separates shared matrix geometry from sample-specific variation, preserves matrix structure, and substantially improves training efficiency. The same framework also handles incomplete training matrices through masked Riemannian updates and iterative completion. Across real and synthetic benchmarks, CoreFlow substantially improves spectral and moment-level generation quality in few-sample regimes while remaining competitive in data-rich settings, even under compression to 9% of the ambient dimension and with up to 40% missing training entries.

Dongze Wu, Linglingzhi Zhu, Yao Xie

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA

Generative Modeling Continuous Normalizing Flows Flow-Based Generative Modeling Matrix Completion

Apr 27, 2026stat.ML

Identifiability and Stability of Generative Drifting with Companion-Elliptic Kernel Families

This paper studies the identifiability and stability of drifting fields in the framework of Generative Modeling via Drifting. The motivating question is whether a zero-drift equilibrium identifies the target distribution and whether an approximately vanishing drift implies weak distributional convergence. Since the original drifting model employs the Laplace kernel by default, we first analyze why Gaussian score-based arguments fail to apply. This analysis motivates the introduction of companion-elliptic kernel families, which are characterized by a companion potential satisfying an elliptic closure relation. We show that this class naturally contains the Laplace kernel and consists precisely of Gaussian and Matérn kernels with smoothness parameter

ν>0

. Within this class, we establish field identifiability for arbitrary Borel probability measures on

R^d

: if the drifting field between two such measures vanishes identically, then they must coincide. For stability, we demonstrate that convergence of the field alone does not guarantee weak convergence, since mass may escape to infinity while remaining invisible to the field. Although tightness directly removes this obstruction and restores weak stability, we prove that, even without tightness, every

C_0

-vague cluster point lies exactly on the defect ray

\{cp:0\le c\le1\}

. Consequently, a single scalar

C_0

observable suffices to detect the missing mass and recover weak convergence.

HakGeun Lee, Hyonho Chun

Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea.

Generative Modeling Convergence Analysis Kernel Methods Drifting Models

Apr 26, 2026cs.AR

FlowPlace: Flow Matching for Chip Placement

Chip placement plays an important role in physical design. While generative models like diffusion models offer promising learning-based solutions, current methods have the following limitations: they use random synthetic data for pre-training, require long sampling times, and often result in overlaps due to their dependence on gradient-based solvers during the sampling process. To overcome these issues, we propose FlowPlace, which features mask-guided synthetic data generation, flow-based efficient training with flexible prior injection, and hard constraint sampling for overlap-free layouts. Experiments on OpenROAD and ICCAD 2015 benchmarks show FlowPlace achieves better PPA metrics, 10-50

\times

faster sampling efficiency, and zero overlaps.

Peng Xie, Ke Xue, Yunqi Shi +6

1State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Artificial Intelligence, Nanjing University, China · 3Huawei Noah’s Ark Lab, China

Constrained Generative Modeling Flow Matching Electronic Design Automation Generative Modeling Flow-Based Generative Modeling

Apr 25, 2026math.NA

GeoFunFlow-3D: A Physics-Guided Generative Flow Matching Framework for High-Fidelity 3D Aerodynamic Inference over Complex Geometries

Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features, primarily due to spectral bias and gradient conflicts within the governing equations. To address these issues, we propose GeoFunFlow-3D, a physics-guided generative flow matching framework. Temporally, we utilize optimal transport theory to build the generation path, ensuring stable training dynamics. Spectrally, we introduce a high-order discrete engine without automatic differentiation (No-AD) to reduce gradient stiffness. Spatially, a topology-aware super-resolution module (SATO) is employed to rigorously enforce physical laws in localized regions such as shock waves. We evaluated our framework on complex industrial datasets. On the BlendedNet dataset, the model successfully avoids mode collapse even under sparse data conditions. For the NASA Rotor37 test, it accurately captures 3D detached shock structures. Compared to conventional operators, GeoFunFlow-3D significantly improves accuracy, reducing the pressure field error (RRMSE) to 0.0215 while maintaining competitive inference efficiency. Ultimately, this work provides a reliable, geometry-driven approach for generating high-dimensional fluid fields.

Ruiling Jiang, Yong Zhang, Houbiao Li

School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

PDE Surrogate Modeling Generative Modeling Computational Fluid Dynamics

Apr 24, 2026cs.CV

BrickNet: Graph-Backed Generative Brick Assembly

We train a language model to generate LEGO-brick build sequences. While prior work has been restricted to discrete, voxel-like towers, we consider a much broader set of pieces, encompassing thousands of part types with diverse connection semantics. To enable this, we first collect a large-scale dataset of over 100,000 human-designed LDraw brick objects and scenes. The complexity of our setting makes it challenging to autoregressively assemble structures that satisfy physical constraints. When predicting block pose directly, build sequences quickly become invalid after a small number of steps. Although pieces are placed in 3D space, it is the spatial relationships of the parts which define the whole. With this in mind, we design a graph-based program representation that parametrizes structure through connectivity, improving the physical grounding of generated sequences. To enable future applications, we make our dataset and models available for research purposes. https://kulits.github.io/BrickNet

Peter Kulits, Cordelia Schmid

Inria, `Ecole Normale Sup`erieure, CNRS, PSL Research University · Max Planck Institute for Intelligent Systems, Tübingen

Constrained Generative Modeling 3D Asset Generation Generative Modeling

Apr 23, 2026cs.LG

Quotient-Space Diffusion Models

Diffusion-based generative models have reformed generative AI, and also enabled new capabilities in the science domain, e.g., fast generation of 3D structures of molecules. In such tasks, there is often a symmetry in the system, identifying elements that can be converted by certain transformations as equivalent. Equivariant diffusion models guarantee a symmetric distribution, but miss the opportunity to make learning easier, while alignment-based simplification attempts fail to preserve the target distribution. In this work, we develop quotient-space diffusion models, a principled generative framework to fully handle and leverage symmetry. By viewing the intrinsic generation process on the quotient space, the exact construction that removes symmetry redundancy, the framework simplifies learning by allowing model output to have an arbitrary intra-equivalence-class movement, while generating the correct symmetric target distribution with guarantee. We instantiate the framework for molecular structure generation which follows

\mathrm{SE}(3)

(rigid-body movement) symmetry. It improves the performance over equivariant diffusion models and outperforms alignment-based methods universally for small molecules and proteins, representing a new framework that surpasses previous symmetry treatments in generative models.

Yixian Xu, Yusong Wang, Shengjie Luo +4

State Key Laboratory of General Artificial Intelligence, Peking University, Beijing, China · State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University · Zhongguancun Academy, Beijing, China +2

Generative Modeling 3D Molecular Generation Molecular Generation Diffusion Models

Apr 22, 2026cs.CV

Materialistic RIR: Material Conditioned Realistic RIR Generation

Rings like gold, thuds like wood! The sound we hear in a scene is shaped not only by the spatial layout of the environment but also by the materials of the objects and surfaces within it. For instance, a room with wooden walls will produce a different acoustic experience from a room with the same spatial layout but concrete walls. Accurately modeling these effects is essential for applications such as virtual reality, robotics, architectural design, and audio engineering. Yet, existing methods for acoustic modeling often entangle spatial and material influences in correlated representations, which limits user control and reduces the realism of the generated acoustics. In this work, we present a novel approach for material-controlled Room Impulse Response (RIR) generation that explicitly disentangles the effects of spatial and material cues in a scene. Our approach models the RIR using two modules: a spatial module that captures the influence of the spatial layout of the scene, and a material module that modulates this spatial RIR according to a user-specified material configuration. This explicitly disentangled design allows users to easily modify the material configuration of a scene and observe its impact on acoustics without altering the spatial structure or scene content. Our model provides significant improvements over prior approaches on both acoustic-based metrics (up to +16% on RTE) and material-based metrics (up to +70%). Furthermore, through a human perceptual study, we demonstrate the improved realism and material sensitivity of our model compared to the strongest baselines.

Mahnoor Fatima Saad, Sagnik Majumder, Kristen Grauman +1

University of Utah · UT Austin

Generative Modeling Conditional Generative Modeling Audio Generation Room Acoustics