Score-Based Generative Modeling

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Score-based generative modeling learns the gradient of a data distribution’s log density, often at multiple noise levels using denoising score matching. Generation then follows learned scores through reverse-time stochastic differential equations, probability-flow ordinary differential equations, or Langevin correctors; extensions handle manifolds, discrete data, and scientific inverse problems. Methods are evaluated on image-generation benchmarks and tasks such as MRI reconstruction, simulation-based inference, and data assimilation, where fidelity, calibration, and sampling cost all matter. A central challenge is connecting score-estimation accuracy to reliable samples: low-noise errors, discretization, initialization, and data geometry can all affect results, while stronger smoothing may reduce memorization but alter fidelity and diversity.

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115 papers16 papers in the last four weeks, up 220% on the four weeks before. 0.1% of all new papers.

Image Modeling: From Handcrafted Priors to Foundation Image Models
Oct 27, 2026A. Murat TekalpImage Inverse Problems Conditional Generative Modeling
Department of Electrical and Electronics Engineering, Koc¸ University, Istanbul, Turkey
Approximation Families and the Statistical Efficiency of Denoising Score Matching
Oct 26, 2026Brian MiyatakeScore Matching Score-Based Generative Modeling
Department of Statistics and Data Science, Yale University
Generative AI in Turbulence: Foundations, Applications, Validations and Benchmarks
Oct 26, 2026Luca Biferale, Michele BuzzicottiGenerative Modeling Generative AI Evaluation
Department of Physics and INFN, University of Rome Tor Vergata, Rome, Italy
OpenMAP-HIE: Pathology Informed Score-based Diffusion Model for Unsupervised Neonatal Hypoxic-Ischemic Encephalopathy Lesion Segmentation
Oct 21, 2026Pengyu Kan, Craig Jones, Kenichi OishiMedical Image Segmentation Medical Image Anomaly Detection
Johns Hopkins University · Johns Hopkins University, University of Alberta · Johns Hopkins University School of Medicine
Diffusion Score Estimation with Shallow Neural Networks: Regularity, Approximation, and Finite-Sample Rates
Oct 19, 2026Fan Liu, Yahong Yang, Wei ZhuScore-Based Generative Modeling Diffusion Models
School of Mathematics, Georgia Institute of Technology, USA · Department of Mathematics and Statistics, Binghamton University, USA
Two-Stage Score Estimation for Group-Specific Diffusion Models
Oct 14, 2026Huitao Yang, Oscar Hernan Madrid PadillaDiffusion Models Score-Based Generative Modeling
University of California, Los Angeles
Denoising Score Matching in Diffusion Models: The Effect of Rank Constraints on Generalization
Oct 14, 2026Anand Jerry George, Nicolas MacrisScore-Based Generative Modeling Neural Network Generalization
École Polytechnique Fédérale de Lausanne (EPFL), Lab for Statistical Mechanics of Inference in Large Systems (SMILS), CH-1015 Lausanne, Switzerland
From Global to Tail Convergence: Dynamics of $α$ -Stable Score-Based Generative Models
Oct 14, 2026Ianis Hammani, Claire BoyerScore-Based Generative Modeling Diffusion Models
ENS Paris Saclay, LMO · LMO, IUF
Discriminative Score Function: Turning Pretrained Models into Functional Generative Priors
Oct 14, 2026Junhoo Lee, Hyeonjin Kim, Sangbum Han +1Generative Modeling Image Generation
Seoul National University
Stein Variational Distributional Reinforcement Learning: Score-Guided Particles for Multivariate Return Distributions
Oct 13, 2026Manuel Haußmann, Melih KandemirDistributional RL Risk-Sensitive RL
University of Southern Denmark
Colored Graph Signal Diffusion Models
Oct 12, 2026Yiğit Berkay Uslu, Samar Hadou, Shirin Saeedi Bidokhti +1Diffusion Models Graph Diffusion
Dept. of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA
A Stochastic Analysis Perspective on Diffusion Models
Oct 9, 2026Stanislas StrasmanScore-Based Generative Modeling Diffusion Sampling
SU, LPSM · Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université
Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis
Oct 8, 2026Adam Perbost, Francis Bach, Pierre MarionDiffusion Sampling Score-Based Generative Modeling
Inria, École normale supérieure – PSL Research University Paris, France
A Unified Score Matching Paradigm for Video Anomaly Detection and Anticipation
Oct 8, 2026Congqi Cao, Zhenhe Liang, Hanwen Zhang +4Video Anomaly Detection Score-Based Generative Modeling
National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology, School of Computer Science, Northwestern Polytechnical University, Xi’an 710129, China · School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710129, China
Gradient-Free Sampling from Generative Models via Stochastic Bounded Extremum Seeking
Oct 3, 2026Alexander ScheinkerDiffusion Sampling Markov Chain Monte Carlo
Instrumentation and Controls Group Los Alamos National Laboratory Los Alamos, NM 87544, USA
Probability flow ODEs in score-based and reflected diffusion models
Oct 2, 2026Rama CONTDiffusion Sampling Diffusion Models
Mathematical Institute, University of Oxford
Sample complexity bounds for categorical Markov random fields via Discrete Diffusions
Oct 1, 2026Shivam Kumar, Nabarun DebMarkov Random Fields Diffusion Sampling
Booth School of Business, University of Chicago
Ornstein-Uhlenbeck Is Hard to Beat, Yet Superlinear Drift Ships Lower Transport Costs
Sep 29, 2026Attila Lovas, Lóránt NagyDiffusion-Based Image Generation Score-Based Generative Modeling
HUN-REN Alfréd Rényi Institute of Mathematics Budapest, Hungary
Weighting Schedules Govern What and When Score-Based Generative Models Learn from Multimodal Data
Sep 28, 2026Jérémie Klinger, Raphaël Urfin, Giulio Biroli +1Generative Modeling Score-Based Generative Modeling
Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005 Paris, France
AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation
Sep 26, 2026Yangwen Zhang, Shiwei Ni, Xiaoping Zhang +2Data Assimilation Bayesian Filtering
School of Mathematical Sciences, Tongji University, Shanghai 200092, China · Department of Information and Computational Sciences, Wuhan University, Wuhan 430072, China · Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA
Quantum score matching with applications to learning thermal states
Sep 23, 2026Yulong Dong, Jiaqi LengQuantum Machine Learning Score-Based Generative Modeling
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA · Institute for Advanced Computing, Virginia Tech, Alexandria, Virginia 22305, USA · Department of Computer Science, Virginia Tech, Alexandria, Virginia 22305, USA
Robustness of Diffusion Models under Distribution Shift
Sep 23, 2026Wei Luo, Neil K. Chada, Shijie Zhang +1Distribution Shift Robustness Diffusion Sampling
Department of Mathematical Sciences, Tsinghua University · Department of Mathematics, City University of Hong Kong, Hong Kong SAR · Artificial Intelligence Research Institute, Shenzhen MSU-BIT University +1
Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds
Sep 15, 2026Jan Tauberschmidt, Brian B. Moser, Stanislav Frolov +3Dynamical Systems Latent Dynamics Modeling
DFKI Kaiserslautern · RPTU Kaiserslautern · Imperial College London
Score-based Outlier Generation via Controlling the Radon-Nikodym Derivative
Sep 10, 2026Amartya Mukherjee, Tristan Milne, Kry Yik-Chau Lui +2Diffusion Sampling Synthetic Anomaly Generation
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 · Royal Bank of Canada, 1 Place Ville Marie, Montreal, Quebec, H3C 3A9
Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime
Aug 25, 2026Hugo Latourelle-Vigeant, Sinho Chewi, Aram-Alexandre Pooladian +2Generative Modeling Score-Based Generative Modeling
Department of Statistics and Data Science, Yale University · Institute for Foundations of Data Science, Yale University · Department of Applied Physics, Yale University
The Loss Floor of Denoising Score Matching: Fisher Geometry from Schrödinger Bridges
Aug 24, 2026Avinash Raju, Kai ZhangScore-Based Generative Modeling Diffusion Models
Great Wall Motors Co. Ltd. Beijing, China · China Patent Information Center Beijing, China
A Theory of Speciation in Generative Diffusion Models on Compact Riemannian Manifolds
Aug 24, 2026Alessio Marta, Paola CausinDiffusion Models Score-Based Generative Modeling
Department of Mathematics, University of Milan, via Saldini 50, 20133 Milan, Italy
STEP: Score-Based Temporal Energy for Human Pose Video Anomaly Detection
Aug 20, 2026Jakub Micorek, Mateusz Koziński, Horst PosseggerVideo Anomaly Detection Energy-Based Models
Institute of Visual Computing, Graz University of Technology, Austria · Institute for Medical Informatics, Statistics and Documentation, Medical University of Graz, Austria
A Plug-in Interpretation of Conditioning in Score-Based Diffusion Models
Aug 19, 2026Libo Chen, Souvik Ghosh, Teo Deveney +2Conditional Diffusion Models Diffusion Model Sampling
University of Bath, Bath, UK · International Institute of Information Technology Hyderabad, India
Information Spreading in Diffusion Models from Effective Field Theory
Aug 14, 2026Navonil Neogi, Nabil IqbalDiffusion Models Score-Based Generative Modeling
Centre for Particle Theory, Department of Mathematical Sciences, Durham University · Institute of Physics, University of Amsterdam · Amsterdam Machine Learning Lab, University of Amsterdam

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Image Modeling: From Handcrafted Priors to Foundation Image Models

A. Murat Tekalp

Department of Electrical and Electronics Engineering, Koc¸ University, Istanbul, Turkey

Image Inverse Problems Conditional Generative Modeling Bayesian Inverse Problems Score-Based Generative Modeling

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This paper unifies six decades of image modeling, evolving from handcrafted mathematical tractable priors to solve inverse problems in imaging to data-driven deep foundation image models for both image generation and solving inverse problems, under a common Bayesian framework that formulates image modeling as an implicit or explicit probabilistic characterization of a data manifold. Every image restoration or generative task fundamentally seeks to answer the same question: What makes an image look like a real image? In the Bayesian framework, this question is encapsulated by the prior probability density p(x), or its more optimization-friendly counterpart, the log-prior log p(x). While early works in solving inverse problems, such as Tikhonov, Total Variation (TV), and Non-local priors relied on explicit handcrafted definitions of log prior to model local smoothness, modern techniques, such as Plug-and-Play (PnP) priors and Denoising Diffusion models, are rooted in algorithmic uncoupling and implicit manifold learning that apply to both inverse problems and conditional image generation. By grounding imaging inverse problems and conditional image generation under a single mathematical engine: the gradient of the log-prior, or the Stein Score Function, we bridge the gap between signal processing and machine learning communities, turning what seems like parallel developments into a single, evolution of image modeling from handcrafted analytical models to models learned from big data, demonstrating that the pursuit of the denoising score is the common thread connecting variational optimization (in MAP estimation) to posterior sampling (in modern foundation image models).