mlsanityData to 7 Oct 2026

Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers

arXiv 2410.14237 ↗First posted 18 Oct 2024cs.LG math.OC stat.MLcited by 14

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a known prior distribution, and second, sampling to recover the original data distribution from noise. Among the various sampling methods, deterministic samplers stand out for their enhanced efficiency. However, analyzing these deterministic samplers presents unique challenges, as they preclude the use of established techniques such as Girsanov's theorem, which are only applicable to stochastic samplers. Furthermore, existing analysis for deterministic samplers usually focuses on specific examples, lacking a generalized approach for general forward processes and various deterministic samplers. Our paper addresses these limitations by introducing a unified convergence analysis framework. To demonstrate the power of our framework, we analyze the variance-preserving (VP) forward process with the exponential integrator (EI) scheme, achieving iteration complexity of tilde O(d2/ε). Additionally, we provide a detailed analysis of Denoising Diffusion Implicit Models (DDIM)-type samplers, which have been underexplored in previous research, achieving polynomial iteration complexity.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 19 of its 40 references that are in the map. First posted on arXiv 18 Oct 2024.

Builds on

19 of 40 references.

Closest ancestors · 12

Same direction, newest first

  1. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  2. 2024Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference26 May
  3. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  4. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  5. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
  6. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis4 Jul
  7. 2023Error Bounds for Flow Matching Methods26 May
  8. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  9. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models31 Aug
  10. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  11. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  12. 2020Denoising Diffusion Implicit Models6 Oct

Other references · 7

  1. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  2. 2022Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learningcited by 543
  3. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  4. 2023A Reparameterized Discrete Diffusion Model for Text Generationcited by 152
  5. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  6. 2024DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Designcited by 87
  7. 2023Fast Sampling via Discrete Non-Markov Diffusion Models with Predetermined Transition Timecited by 20

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 9; 2026: 5.

14 papers.

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  1. 2025Low-dimensional adaptation of diffusion models: Convergence in total variationcited by 38
  2. 2025Discrete Diffusion Models: Novel Analysis and New Sampler Guaranteescited by 20
  3. 2025Faster Diffusion Models via Higher-Order Approximationcited by 16
  4. 2025Optimal Convergence Analysis of DDPM for General Distributionscited by 16
  5. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Modelscited by 9
  6. 2025Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Modelscited by 8
  7. 2025A Sharp KL-Convergence Analysis for Diffusion Models under Minimal Assumptionscited by 8
  8. 2026Sharp Convergence Rates for Masked Diffusion Modelscited by 8
  9. 2025Multi-Step Consistency Models: Fast Generation with Theoretical Guaranteescited by 2
  10. 2025Finite-Time Convergence Analysis of ODE-based Generative Models for Stochastic Interpolantscited by 1
  11. 2026Provably Reliable Classifier Guidance via Cross-Entropy Controlcited by 1
  12. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplerscited by 1
2 more
  1. 2026On the Robustness of Distribution Support under Diffusion Guidancecited by 1
  2. 2026Diffusion Models for Adaptive Sequential Data Generationcited by 1

Similar, not cited

Close in wording, no citation either way

  1. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  2. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers
  3. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Models
  4. 2024Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis
  5. 2023Denoising Diffusion Samplers
  6. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
  7. 2024Provable Acceleration for Diffusion Models under Minimal Assumptions
  8. 2025On the Collapse Errors Induced by the Deterministic Sampler for Diffusion Models