mlsanityData to 13 Oct 2026

Practical and Asymptotically Exact Conditional Sampling in Diffusion Models

arXiv 2306.17775 ↗First posted 30 Jun 2023stat.ML cs.LG q-bio.BMcited by 227

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models through simulating a set of weighted particles. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and in conditional image generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state of the art.

Key facts. Cited by 227 papers in the map (data through 13 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 21 of its 40 references that are in the map. First posted on arXiv 30 Jun 2023.

Builds on

21 of 40 references.

Closest ancestors · 2

Same direction, newest first

  1. 2023SE(3) diffusion model with application to protein backbone generation5 Feb
  2. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun

Other references · 19

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,952
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,028
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,213
  4. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,564
  5. 2022Classifier-Free Diffusion Guidancecited by 5,785
  6. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,023
  7. 2022Video Diffusion Modelscited by 2,293
  8. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,921
  9. 2021Image Super-Resolution via Iterative Refinementcited by 1,509
  10. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,425
  11. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,403
  12. 2021Palette: Image-to-Image Diffusion Modelscited by 1,298
7 more
  1. 2022Denoising Diffusion Restoration Modelscited by 958
  2. 2023Universal Guidance for Diffusion Modelscited by 434
  3. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 219
  4. 2022Riemannian Score-Based Generative Modellingcited by 217
  5. 2019Elements of Sequential Monte Carlocited by 64
  6. 2023Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Modelscited by 61
  7. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 59

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 9; 2024: 40; 2025: 80; 2026: 98.

227 papers.

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  1. 2024A Survey on Diffusion Models for Inverse Problemscited by 179
  2. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 134
  3. 2023Stochastic interpolants with data-dependent couplingscited by 97
  4. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 95
  5. 2025Test-time Alignment of Diffusion Models without Reward Over-optimizationcited by 93
  6. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 92
  7. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 76
  8. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  9. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 68
  10. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problemscited by 66
  11. 2024Particle Denoising Diffusion Samplercited by 65
  12. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 61
38 more
  1. 2024Estimating Epistemic and Aleatoric Uncertainty with a Single Modelcited by 53
  2. 2025Inference-time Scaling of Diffusion Models through Classical Searchcited by 49
  3. 2024Sequential Controlled Langevin Diffusionscited by 47
  4. 2024Improved motif-scaffolding with SE(3) flow matchingcited by 43
  5. 2025Inference-Time Text-to-Video Alignment with Diffusion Latent Beam Searchcited by 40
  6. 2025Scaling Image and Video Generation via Test-Time Evolutionary Searchcited by 39
  7. 2025Fine-Tuning Discrete Diffusion Models with Policy Gradient Methodscited by 38
  8. 2025Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcingcited by 38
  9. 2025Dynamic Search for Inference-Time Alignment in Diffusion Modelscited by 36
  10. 2026Meta Flow Maps enable scalable reward alignmentcited by 36
  11. 2024Diffusion Models as Constrained Samplers for Optimization with Unknown Constraintscited by 35
  12. 2024Out of Many, One: Designing and Scaffolding Proteins at the Scale of the Structural Universe with Genie 2cited by 34
  13. 2025Diffusion Tree Sampling: Scalable inference-time alignment of diffusion modelscited by 33
  14. 2024Variational Diffusion Posterior Sampling with Midpoint Guidancecited by 32
  15. 2026Inference-time Physics Alignment of Video Generative Models with Latent World Modelscited by 32
  16. 2024Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNetscited by 30
  17. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlocited by 30
  18. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priorscited by 28
  19. 2026Diamond Maps: Efficient Reward Alignment via Stochastic Flow Mapscited by 28
  20. 2025Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Designcited by 25
  21. 2024ProteinBench: A Holistic Evaluation of Protein Foundation Modelscited by 24
  22. 2025Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Modelscited by 23
  23. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  24. 2025SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationscited by 22
  25. 2023Neural Diffusion Modelscited by 21
  26. 2025Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posteriorcited by 21
  27. 2024Diffusion Posterior Sampling is Computationally Intractablecited by 20
  28. 2024Conditional sampling within generative diffusion modelscited by 18
  29. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  30. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  31. 2025RNE: plug-and-play diffusion inference-time control and energy-based trainingcited by 17
  32. 2025GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Modelscited by 17
  33. 2024Adding Conditional Control to Diffusion Models with Reinforcement Learningcited by 16
  34. 2025Lookahead Unmasking Elicits Accurate Decoding in Diffusion Language Modelscited by 16
  35. 2025Test-time scaling of diffusions with flow mapscited by 16
  36. 2023Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstructioncited by 15
  37. 2023Correcting Diffusion Generation through Resamplingcited by 15
  38. 2025Psi-Sampler: Initial Particle Sampling for SMC-Based Inference-Time Reward Alignment in Score Modelscited by 15

50 most cited of 227 All 227 (JSON)

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  1. 2026Probing the Geometry of Diffusion Models with the String Method
  2. 2024Conditional Synthesis of 3D Molecules with Time Correction Sampler
  3. 2026Enhanced Diffusion Sampling: Efficient Rare Event Sampling and Free Energy Calculation with Diffusion Models
  4. 2024Context-Guided Diffusion for Out-of-Distribution Molecular and Protein Design
  5. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Review
  6. 2026Specificity-Aware Diffusion Steering via Variance-Reduced Sequential Monte Carlo
  7. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models
  8. 2026Breaking the Bottlenecks: Scalable Diffusion Models for 3D Molecular Generation