mlsanityData to 13 Oct 2026

Conditional sampling within generative diffusion models

arXiv 2409.09650 ↗First posted 15 Sep 2024stat.ML cs.LGcited by 18

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their success in these domains, an important open challenge remains: extending these techniques to sample from conditional distributions, as required in, for example, Bayesian inverse problems. In this paper, we present a comprehensive review of existing computational approaches to conditional sampling within generative diffusion models. Specifically, we highlight key methodologies that either utilise the joint distribution, or rely on (pre-trained) marginal distributions with explicit likelihoods, to construct conditional generative samplers.

Key facts. Cited by 18 papers in the map (data through 13 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 26 of its 47 references that are in the map. First posted on arXiv 15 Sep 2024.

Builds on

26 of 47 references.

Closest ancestors · 11

Same direction, newest first

  1. 2024Conditioning diffusion models by explicit forward-backward bridging22 May
  2. 2024Particle Denoising Diffusion Sampler9 Feb
  3. 2023Diffusion Schr"odinger Bridge Matching29 Mar
  4. 2023Denoising Diffusion Samplers27 Feb
  5. 2022From Denoising Diffusions to Denoising Markov Models7 Nov
  6. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  7. 2022Conditional Simulation Using Diffusion Schr"odinger Bridges27 Feb
  8. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality11 Feb
  9. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 15

  1. 2022Flow Matching for Generative Modelingcited by 5,542
  2. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,425
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,403
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,317
  5. 2022Denoising Diffusion Restoration Modelscited by 958
  6. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 234
  7. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 227
  8. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 218
  9. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 217
  10. 2023Image Restoration with Mean-Reverting Stochastic Differential Equationscited by 183
  11. 2023Aligned Diffusion Schr"odinger Bridgescited by 38
  12. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priorscited by 28
3 more
  1. 2016Auxiliary gradient-based sampling algorithmscited by 21
  2. 2022An energy-based deep splitting method for the nonlinear filtering problemcited by 7
  3. 2019Unbiased Smoothing using Particle Independent Metropolis-Hastingscited by 6

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2025: 13; 2026: 5.

18 papers.

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  1. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 217
  2. 2025Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlocited by 20
  3. 2025Conditioning Diffusions Using Malliavin Calculuscited by 15
  4. 2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlocited by 10
  5. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 7
  6. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 5
  7. 2025DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolantscited by 5
  8. 2025Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusionscited by 4
  9. 2025Generative diffusion posterior sampling for informative likelihoodscited by 4
  10. 2026Particle-Guided Diffusion Models for Partial Differential Equationscited by 4
  11. 2026Supervised Guidance Training for Infinite-Dimensional Diffusion Modelscited by 3
  12. 2025Diffusion differentiable resamplingcited by 2
6 more
  1. 2025On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reductioncited by 2
  2. 2025Diffusion models for multivariate subsurface generation and efficient probabilistic inversioncited by 1
  3. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  4. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a surveycited by 0
  5. 2026Coarse-Grained Kullback--Leibler Control of Diffusion-Based Generative AIcited by 0
  6. 2026Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Samplingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Generative Uncertainty in Diffusion Models
  2. 2025Generative Modeling with Bayesian Sample Inference
  3. 2022Bi-Noising Diffusion: Towards Conditional Diffusion Models with Generative Restoration Priors
  4. 2026Generative and Nonparametric Approaches for Conditional Distribution Estimation: Methods, Perspectives, and Comparative Evaluations
  5. 2025Information-Theoretic Proofs for Diffusion Sampling
  6. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory
  7. 2025Diffusion Models: A Mathematical Introduction
  8. 2025Diffusion-based supervised learning of generative models for efficient sampling of multimodal distributions