# Posterior sampling via Langevin dynamics based on generative priors

arXiv: https://arxiv.org/abs/2410.02078 · HTML: https://mlsanity.com/paper/2410.02078/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 53 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 30 of 46)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [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)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)

## Built on by (most cited first, 5 of 5)

- [Provable Acceleration for Diffusion Models under Minimal Assumptions](https://mlsanity.com/paper/2410.23285/) (2024)
- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Generative models for decision-making under distributional shift](https://mlsanity.com/paper/2604.04342/) (2026)
- [Sparse Fine-Tuning of Transformers for Generative Tasks](https://mlsanity.com/paper/2507.10855/) (2025)
- [Energy-Based Models for Predicting Mutational Effects on Proteins](https://mlsanity.com/paper/2508.10629/) (2025)

## Abstract (arXiv)

Posterior sampling in high-dimensional spaces using generative models holds significant promise for various applications, including but not limited to inverse problems and guided generation tasks. Despite many recent developments, generating diverse posterior samples remains a challenge, as existing methods require restarting the entire generative process for each new sample, making the procedure computationally expensive. In this work, we propose efficient posterior sampling by simulating Langevin dynamics in the noise space of a pre-trained generative model. By exploiting the mapping between the noise and data spaces which can be provided by distilled flows or consistency models, our method enables seamless exploration of the posterior without the need to re-run the full sampling chain, drastically reducing computational overhead. Theoretically, we prove a guarantee for the proposed noise-space Langevin dynamics to approximate the posterior, assuming that the generative model sufficiently approximates the prior distribution. Our framework is experimentally validated on image restoration tasks involving noisy linear and nonlinear forward operators applied to LSUN-Bedroom (256 x 256) and ImageNet (64 x 64) datasets. The results demonstrate that our approach generates high-fidelity samples with enhanced semantic diversity even under a limited number of function evaluations, offering superior efficiency and performance compared to existing diffusion-based posterior sampling techniques.