# Conditional sampling within generative diffusion models

arXiv: https://arxiv.org/abs/2409.09650 · HTML: https://mlsanity.com/paper/2409.09650/

## Key facts

- Cited by 19 papers in the map (data through 14 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.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 26 of 26)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [Particle Denoising Diffusion Sampler](https://mlsanity.com/paper/2402.06320/) (2024)
- [Conditional Simulation Using Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2202.13460/) (2022)
- [From Denoising Diffusions to Denoising Markov Models](https://mlsanity.com/paper/2211.03595/) (2022)
- [Aligned Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2302.11419/) (2023)
- [Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors](https://mlsanity.com/paper/2403.11407/) (2024)
- [Auxiliary gradient-based sampling algorithms](https://mlsanity.com/paper/1610.09641/) (2016)
- [Conditioning diffusion models by explicit forward-backward bridging](https://mlsanity.com/paper/2405.13794/) (2024)
- [An energy-based deep splitting method for the nonlinear filtering problem](https://mlsanity.com/paper/2203.17153/) (2022)
- [Unbiased Smoothing using Particle Independent Metropolis-Hastings](https://mlsanity.com/paper/1902.01781/) (2019)

## Built on by (most cited first, 19 of 19)

- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo](https://mlsanity.com/paper/2502.12786/) (2025)
- [Conditioning Diffusions Using Malliavin Calculus](https://mlsanity.com/paper/2504.03461/) (2025)
- [Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo](https://mlsanity.com/paper/2502.06379/) (2025)
- [ESS-Flow: Training-free guidance of flow-based models as inference in source space](https://mlsanity.com/paper/2510.05849/) (2025)
- [Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priors](https://mlsanity.com/paper/2510.10968/) (2025)
- [DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants](https://mlsanity.com/paper/2512.00252/) (2025)
- [Particle-Guided Diffusion Models for Partial Differential Equations](https://mlsanity.com/paper/2601.23262/) (2026)
- [Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions](https://mlsanity.com/paper/2501.19373/) (2025)
- [Generative diffusion posterior sampling for informative likelihoods](https://mlsanity.com/paper/2506.01083/) (2025)
- [On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reduction](https://mlsanity.com/paper/2512.18971/) (2025)
- [Supervised Guidance Training for Infinite-Dimensional Diffusion Models](https://mlsanity.com/paper/2601.20756/) (2026)
- [Diffusion differentiable resampling](https://mlsanity.com/paper/2512.10401/) (2025)
- [LatentFlow: A General Framework for Conditioning Stochastic Processes](https://mlsanity.com/paper/2607.12922/) (2026)
- [Diffusion models for multivariate subsurface generation and efficient probabilistic inversion](https://mlsanity.com/paper/2507.15809/) (2025)
- [Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey](https://mlsanity.com/paper/2510.14114/) (2025)
- [Coarse-Grained Kullback--Leibler Control of Diffusion-Based Generative AI](https://mlsanity.com/paper/2601.01045/) (2026)
- [Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Sampling](https://mlsanity.com/paper/2604.16461/) (2026)
- [Sampling from Neural Operator Priors to Solve Partial Differential Equations](https://mlsanity.com/paper/2610.16396/) (2026)

## 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.