mlsanityData to 14 Oct 2026

On Forgetting and Stability of Score-based Generative models

arXiv 2601.21868 ↗First posted 29 Jan 2026stat.ML cs.LGcited by 5

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging stability and forgetting properties of the Markov chain associated with the reverse-time dynamics. Under weak assumptions, we provide the two structural properties to ensure the propagation of initialization and discretization errors of the backward process: a Lyapunov drift condition and a Doeblin-type minorization condition. A practical consequence is quantitative stability of the sampling procedure, as the reverse diffusion dynamics induces a contraction mechanism along the sampling trajectory. Our results clarify the role of stochastic dynamics in score-based models and provide a principled framework for analyzing propagation of errors in such approaches.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 24 of its 42 references that are in the map. First posted on arXiv 29 Jan 2026.

Builds on

24 of 42 references.

Closest ancestors · 13

Same direction, newest first

  1. 2025Wasserstein Convergence of Critically Damped Langevin Diffusions4 Nov
  2. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance5 Aug
  3. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients6 May
  4. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration7 Feb
  5. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance4 Jan
  6. 2024An analysis of the noise schedule for score-based generative models7 Feb
  7. 2024Contractive Diffusion Probabilistic Models23 Jan
  8. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  9. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  10. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  12. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
1 more
  1. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 11

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2017Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysiscited by 243
  4. 2019Generalized Sliced Wasserstein Distancescited by 208
  5. 2015Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithmcited by 197
  6. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  7. 2022Improved analysis for a proximal algorithm for samplingcited by 73
  8. 2017A Hitting Time Analysis of Stochastic Gradient Langevin Dynamicscited by 71
  9. 2020On the Convergence of Langevin Monte Carlo: The Interplay between Tail Growth and Smoothnesscited by 55
  10. 2020Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergencecited by 42
  11. 2024Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusioncited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Samplingcited by 2
  2. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplerscited by 1
  3. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Modelscited by 1
  4. 2026A Stochastic Analysis Perspective on Diffusion Modelscited by 0
  5. 2026Radial Tail Repair: Post-Training Correction for Diffusion and Flow Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026From Global to Tail Convergence: Dynamics of α-Stable Score-Based Generative Models
  2. 2023Improved Convergence of Score-Based Diffusion Models via Prediction-Correction
  3. 2024Score-based generative models are provably robust: an uncertainty quantification perspective
  4. 2026Modeling Score Approximation Errors in Diffusion Models via Forward SPDEs
  5. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
  6. 2026From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models
  7. 2022Convergence for score-based generative modeling with polynomial complexity
  8. 2024Discrete vs. Continuous Trade-offs for Generative Models