mlsanityData to 7 Oct 2026

SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models

arXiv 2309.05019 ↗First posted 10 Sep 2023cs.LG stat.MLcited by 71

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose textitSA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that textitSA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art (SOTA) sampling methods for few-step sampling; 2) SOTA FID on substantial benchmark datasets under a suitable number of function evaluations (NFEs). Code is available at https://github.com/scxue/SA-Solver.

Key facts. Cited by 71 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 31 of its 44 references that are in the map. First posted on arXiv 10 Sep 2023.

Builds on

31 of 44 references.

Closest ancestors · 21

Same direction, newest first

  1. 2023Efficient Diffusion Training via Min-SNR Weighting Strategy16 Mar
  2. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models9 Feb
  3. 2023ERA-Solver: Error-Robust Adams Solver for Fast Sampling of Diffusion Probabilistic Models30 Jan
  4. 2022Scalable Diffusion Models with Transformers19 Dec
  5. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  6. 2022On Distillation of Guided Diffusion Models6 Oct
  7. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  8. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  9. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  10. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality11 Feb
  11. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  12. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
9 more
  1. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  2. 2021Variational Diffusion Models1 Jul
  3. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  4. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  5. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  6. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
  7. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  8. 2020Denoising Diffusion Implicit Models6 Oct
  9. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 10

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  4. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,595
  5. 2022Video Diffusion Modelscited by 2,280
  6. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  7. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  8. 2022Diffusion-GAN: Training GANs with Diffusioncited by 203
  9. 2022BDDM: Bilateral Denoising Diffusion Models for Fast and High-Quality Speech Synthesiscited by 64
  10. 2022Transcormer: Transformer for Sentence Scoring with Sliding Language Modelingcited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 28; 2025: 27; 2026: 11.

71 papers.

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  1. 2023PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesiscited by 854
  2. 2024Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generationcited by 211
  3. 2024Consistency Models Made Easycited by 140
  4. 2024Accelerating Convergence of Score-Based Diffusion Models, Provablycited by 74
  5. 2023VideoSwap: Customized Video Subject Swapping with Interactive Semantic Point Correspondencecited by 69
  6. 2024One-Step Diffusion Distillation through Score Implicit Matchingcited by 68
  7. 2024Accelerating Diffusion Sampling with Optimized Time Stepscited by 67
  8. 2023The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editingcited by 61
  9. 2025Advantage Weighted Matching: Aligning RL with Pretraining in Diffusion Modelscited by 59
  10. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  11. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Modelscited by 35
  12. 2025Efficient Diffusion Models: A Surveycited by 35
38 more
  1. 2024DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Spacecited by 32
  2. 2024Diff-Instruct++: Training One-step Text-to-image Generator Model to Align with Human Preferencescited by 30
  3. 2024Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equationscited by 28
  4. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  5. 2024Flow Generator Matchingcited by 26
  6. 2024Towards a mathematical theory for consistency training in diffusion modelscited by 25
  7. 2024Efficient Diffusion Transformer with Step-wise Dynamic Attention Mediatorscited by 24
  8. 2024Self-Guidance: Boosting Flow and Diffusion Generation on Their Owncited by 22
  9. 2025Reward-Instruct: A Reward-Centric Approach to Fast Photo-Realistic Image Generationcited by 19
  10. 2024HarmoniCa: Harmonizing Training and Inference for Better Feature Caching in Diffusion Transformer Accelerationcited by 16
  11. 2025Gaussian Mixture Flow Matching Modelscited by 16
  12. 2025Faster Diffusion Models via Higher-Order Approximationcited by 16
  13. 2025Optimal Convergence Analysis of DDPM for General Distributionscited by 16
  14. 2025Consistency Trajectory Matching for One-Step Generative Super-Resolutioncited by 15
  15. 2025Ultra-Fast Language Generation via Discrete Diffusion Divergence Instructcited by 15
  16. 2024The Surprising Effectiveness of Skip-Tuning in Diffusion Samplingcited by 13
  17. 2025FlexiDiT: Your Diffusion Transformer Can Easily Generate High-Quality Samples with Less Computecited by 12
  18. 2025Accelerating Diffusion Transformer via Increment-Calibrated Caching with Channel-Aware Singular Value Decompositioncited by 12
  19. 2023Efficient Integrators for Diffusion Generative Modelscited by 11
  20. 2024DC-Solver: Improving Predictor-Corrector Diffusion Sampler via Dynamic Compensationcited by 11
  21. 2024NAF-DPM: A Nonlinear Activation-Free Diffusion Probabilistic Model for Document Enhancementcited by 9
  22. 2024Variational Schr"odinger Diffusion Modelscited by 9
  23. 2024Structured Diffusion Models with Mixture of Gaussians as Prior Distributioncited by 8
  24. 2024David and Goliath: Small One-step Model Beats Large Diffusion with Score Post-trainingcited by 8
  25. 2025Straight-Line Diffusion Model for Efficient 3D Molecular Generationcited by 8
  26. 2025Learnable Sampler Distillation for Discrete Diffusion Modelscited by 8
  27. 2023Elucidating the solution space of extended reverse-time SDE for diffusion modelscited by 7
  28. 2024PFDiff: Training-Free Acceleration of Diffusion Models Combining Past and Future Scorescited by 7
  29. 2025Federated Learning for Diffusion Modelscited by 6
  30. 2025Adaptive Stochastic Coefficients for Accelerating Diffusion Samplingcited by 6
  31. 2024Learning Efficient and Effective Trajectories for Differential Equation-based Image Restorationcited by 5
  32. 2025Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolationcited by 4
  33. 2025Improved Diffusion-based Generative Model with Better Adversarial Robustnesscited by 3
  34. 2026Q-Drift: Quantization-Aware Drift Correction for Diffusion Model Samplingcited by 3
  35. 2026SHIFT: Stochastic Hidden-Trajectory Deflection for Removing Diffusion-based Watermarkcited by 3
  36. 2025PCM : Picard Consistency Model for Fast Parallel Sampling of Diffusion Modelscited by 2
  37. 2025TADA: Improved Diffusion Sampling with Training-free Augmented Dynamicscited by 2
  38. 2025Deep Neural Networks Inspired by Differential Equationscited by 2

50 most cited of 71 All 71 (JSON)

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  1. 2023A Unified Sampling Framework for Solver Searching of Diffusion Probabilistic Models
  2. 2023SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models
  3. 2023A Geometric Perspective on Diffusion Models
  4. 2024Optimizing Few-Step Sampler for Diffusion Probabilistic Model
  5. 2026Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling
  6. 2023Sampler Scheduler for Diffusion Models
  7. 2025MaRS: A Fast Sampler for Mean Reverting Diffusion based on ODE and SDE Solvers
  8. 2023Fast ODE-based Sampling for Diffusion Models in Around 5 Steps