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.

Latest papers

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

Adapting a Pre-trained Single-Cell Foundation Model to Spatial Gene Expression Generation from Histology Images
Mar 20, 2026Donghai Fang, Yongheng Li, Zhen Wang +2Gene Expression Prediction from Histopathology Images Spatial Transcriptomics
Sun Yat-sen University, China · Yunnan University, China · Chongqing University, China
On the Robustness of Langevin Dynamics to Score Function Error
Mar 11, 2026Daniel Yiming Cao, August Y. Chen, Karthik Sridharan +1Langevin Dynamics Score-Based Generative Modeling
Cornell University, Ithaca, USA
Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework
Mar 10, 2026Rajesh Shrestha, Xiao FuDiffusion-Based Inverse Problems Inverse Problems
School of EECS, Oregon State University
A Unified View of Score-Based and Drifting Models
Mar 8, 2026Chieh-Hsin Lai, Bac Nguyen, Naoki Murata +5Generative Modeling Drifting Models
Sony AI · Sony Group Corporation · Stanford University +1
3D CBCT Artefact Removal Using Perpendicular Score-Based Diffusion Models
Mar 6, 2026Susanne Schaub, Florentin Bieder, Matheus L. Oliveira +4Cone-Beam CT Computed Tomography
Department of Biomedical Engineering, University of Basel, Allschwil, Switzerland · Piracicaba Dental School, University of Campinas, Piracicaba, Brazil · State Key Laboratory of Oral & Maxillofacial Reconstruction and Regeneration, Key Laboratory of Oral Biomedicine Ministry of Education, Hubei Key Laboratory of Stomatology, School & Hospital of Stomatology, Wuhan University, Wuhan, China +2
Score-Guided Proximal Projection: A Unified Geometric Framework for Rectified Flow Editing
Mar 5, 2026Vansh Bansal, James G ScottProximal Optimization Rectified Flow
Department of Statistics and Data Sciences, UT Austin
Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
Mar 4, 2026Saptarshi Chakraborty, Quentin Berthet, Peter L. BartlettScore-Based Generative Modeling Diffusion Models
Department of Statistics, University of Michigan · Google DeepMind · Department of Statistics, University of California, Berkeley +1
Manifold Aware Denoising Score Matching (MAD)
Mar 2, 2026Alona Levy-Jurgenson, Alvaro Prat, James Cuin +1Score-Based Generative Modeling Generative Modeling
Department of Statistics University of Oxford · Department of Mathematics, Imperial College London, London, United Kingdom
Generalizing Score-based generative models for Heavy-tailed Distributions
Feb 28, 2026Tiziano Fassina, Gabriel Cardoso, Sylvan Le Corff +1Generative Modeling Score-Based Generative Modeling
STIM, Mines Paris Paris, France · LPSM, Sorbonne Université Paris, France
Quantifying Error Propagation and Model Collapse in Diffusion Models
Feb 18, 2026Nail B. Khelifa, Richard E. Turner, Ramji VenkataramananModel Collapse Diffusion Models
University of Cambridge, Cambridge, United Kingdom.
Score-based diffusion models for severely ill-posed problems in diffuse optical tomography
Feb 3, 2026Fabian Schneider, Meghdoot Mozumder, Konstantin Tamarov +4Medical Imaging Bayesian Inverse Problems
Department of Computational Engineering, School of Engineering Science LUT University, Finland. · Institute of Analysis and Scientific Computing, TU Wien, Austria. · Department of Technical Physics, Faculty of Science, Forestry and Technology, University of Eastern Finland, Finland. +1
Smoothing the Score Function to Enhance Generalization in Diffusion Models
Jan 27, 2026Xinyu Zhou, Jiawei Zhang, Stephen J. WrightMemorization in Generative Models Generative Modeling
Department of Computer Sciences, University of Wisconsin Madison, WI, USA.
Fast Score-Based Sampling via Log-Concave Reductions
Dec 30, 2025M. J. WainwrightSample Complexity Log-Concave Sampling
Laboratory for Information and Decision Systems · Statistics and Data Science Center · EECS & Mathematics +1
Control Variate Score Matching for Diffusion Models
Dec 23, 2025Khaled Kahouli, Romuald Elie, Klaus-Robert Müller +3Score Matching Sampling from Unnormalized Distributions
1Google DeepMind · 2BIFOLD – Berlin Institute for the Foundations of Learning and Data · 3Machine Learning Group, Technische Universität Berlin +2
Diffusion Models in Simulation-Based Inference: A Tutorial Review
Dec 22, 2025Jonas Arruda, Niels Bracher, Ullrich Köthe +2Simulation-Based Inference Parameter Estimation
Bonn Center for Mathematical Life Sciences, Life & Medical Sciences Institute, University of Bonn, Germany · Center for Modeling, Simulation, & Imaging in Medicine (CeMSIM), Rensselaer Polytechnic Institute, NY, USA · Computer Vision and Learning Lab, Heidelberg University, Germany
Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions
Dec 7, 2025Kaichen Shen, Wei ZhuScore-Based Generative Modeling Diffusion Models
School of Mathematics, Georgia Institute of Technology, Atlanta, GA
A PDE Perspective on Generative Diffusion Models
Nov 8, 2025Kang Liu, Enrique ZuazuaFokker–Planck Equation Diffusion Models
Universit´e Bourgogne Europe, CNRS, Institut de Mathematiques de Bourgogne, 21000 Dijon, France. · Friedrich - Alexander - Universität Erlangen - Nürnberg, Department of Mathematics, Chair for Dynamics, Control, Machine Learning, and Numerics (Alexander von Humboldt Professorship), 91058 Erlangen, Germany. · Universidad Aut´onoma de Madrid, Departamento de Matem´aticas, 28049 Madrid, Spain. +1
Local Learning Rules for Out-of-Equilibrium Physical Generative Models
Jun 23, 2025Cyrill Bösch, Geoffrey Roeder, Marc Serra-Garcia +1Generative Modeling Score-Based Generative Modeling
Department of Computer Science, Princeton University, Princeton, NJ 08540, USA · AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis
Jun 13, 2025Bernardo P. Schaeffer, Ricardo M. S. Rosa, Glauco ValleStochastic Differential Equations Diffusion Sampling
Instituto de Matem´atica, Universidade Federal do Rio de Janeiro
ScoreMix: Synthetic Data Generation by Score Composition in Diffusion Models Improves Recognition
Jun 11, 2025Parsa Rahimi, Sebastien MarcelSynthetic Data Augmentation Synthetic Data Generation
1EPFL, Switzerland · 2Idiap, Switzerland
Score-Based Training for Energy-Based TTS Models
May 19, 2025Wanli Sun, Anton RagniEnergy-Based Models Score Matching
School of Computer Science, University of Sheffield, Sheffield, UK
Localized Diffusion Models
May 7, 2025Georg A. Gottwald, Shuigen Liu, Youssef Marzouk +2Curse of Dimensionality Score-Based Generative Modeling
School of Mathematics and Statistics, The University of Sydney · Department of Mathematics, National University of Singapore · Laboratory for Information and Decision Systems, Massachusetts Institute of Technology +1
Riemannian Denoising Diffusion Probabilistic Models
May 7, 2025Zichen Liu, Wei Zhang, Christof Schütte +1Generative Modeling Score-Based Generative Modeling
Center for Data Science, Peking University, Beijing 100871, P.R. China · Zuse Institute Berlin, Takustrasse 7, Berlin 14195, Germany · Institute of Mathematics, Freie Universität Berlin and Zuse Institute Berlin, Takustrasse 7, Berlin 14195, Germany +1
Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
Oct 2, 2024Ziyu Chen, Markos A. Katsoulakis, Benjamin J. ZhangFlow Matching Equivariant Neural Networks
Department of Mathematics and School of Data and Information Sciences, University of North Carolina at Chapel Hill · Department of Mathematics and Statistics, University of Massachusetts Amherst · Department of Mathematics, Rutgers University–New Brunswick
Adaptive Momentum Benefits Score-based Generative Models
May 22, 2024Ziqing Wen, Ping Luo, Jiahuan Wang +3Diffusion Model Acceleration Score-Based Generative Modeling
College of Computer, National University of Defense Technology

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Adapting a Pre-trained Single-Cell Foundation Model to Spatial Gene Expression Generation from Histology Images

Donghai Fang, Yongheng Li, Zhen Wang, Yuansong Zeng+1

Sun Yat-sen University, China · Yunnan University, China · Chongqing University, China

Gene Expression Prediction from Histopathology Images Spatial Transcriptomics Conditional Generative Modeling Score-Based Generative Modeling

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Spatial transcriptomics (ST) enables spot-level in situ expression profiling, but its high cost and limited throughput motivate predicting expression directly from HE-stained histology. Recent advances explore using score- or flow-based generative models to estimate the conditional distribution of gene expression from histology, offering a flexible alternative to deterministic regression approaches. However, most existing generative approaches omit explicit modeling of gene-gene dependencies, undermining biological coherence. Single-cell foundation models (sc-FMs), pre-trained across diverse cell populations, capture these critical gene relationships that histology alone cannot reveal. Yet, applying expression-only sc-FMs to histology-conditioned expression modeling is nontrivial due to the absence of a visual pathway, a mismatch between their pre-training and conditional ST objectives, and the scarcity of mixed-cell ST supervision. To address these challenges, we propose HINGE (HIstology-coNditioned GEneration), which retrofits a pre-trained sc-FM into a conditional expression generator while mostly preserving its learned gene relationships. We achieve this by introducing SoftAdaLN, a lightweight, identity-initialized modulation that injects layer-wise visual context into the backbone, coupled with an expression-space masked diffusion objective and a warm-start curriculum to ensure objective alignment and training stability. Evaluated on three ST datasets, ours outperforms state-of-the-art baselines on mean Pearson correlation and yields more accurate spatial marker expression patterns and higher pairwise co-expression consistency, establishing a practical route to adapt pre-trained sc-FMs for histology-conditioned spatial expression generation.