# Solving Bayesian inverse problems with diffusion priors and off-policy RL

arXiv: https://arxiv.org/abs/2503.09746 · HTML: https://mlsanity.com/paper/2503.09746/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 32 of its 53 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)
- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Efficient Diffusion Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2305.20081/) (2023)
- [Likelihood-Based Diffusion Language Models](https://mlsanity.com/paper/2305.18619/) (2023)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [VarGrad: A Low-Variance Gradient Estimator for Variational Inference](https://mlsanity.com/paper/2010.10436/) (2020)
- [Amortizing intractable inference in diffusion models for vision, language, and control](https://mlsanity.com/paper/2405.20971/) (2024)
- [Improved off-policy training of diffusion samplers](https://mlsanity.com/paper/2402.05098/) (2024)

## Abstract (arXiv)

This paper presents a practical application of Relative Trajectory Balance (RTB), a recently introduced off-policy reinforcement learning (RL) objective that can asymptotically solve Bayesian inverse problems optimally. We extend the original work by using RTB to train conditional diffusion model posteriors from pretrained unconditional priors for challenging linear and non-linear inverse problems in vision, and science. We use the objective alongside techniques such as off-policy backtracking exploration to improve training. Importantly, our results show that existing training-free diffusion posterior methods struggle to perform effective posterior inference in latent space due to inherent biases.