# Integrating Amortized Inference with Diffusion Models for Learning Clean Distribution from Corrupted Images

arXiv: https://arxiv.org/abs/2407.11162 · HTML: https://mlsanity.com/paper/2407.11162/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [A Comprehensive Survey on Knowledge Distillation of Diffusion Models](https://mlsanity.com/paper/2304.04262/) (2023)
- [Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data](https://mlsanity.com/paper/2305.01166/) (2023)
- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior](https://mlsanity.com/paper/2309.01949/) (2023)
- [AmbientFlow: Invertible generative models from incomplete, noisy measurements](https://mlsanity.com/paper/2309.04856/) (2023)

## Built on by (most cited first, 12 of 12)

- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [One-Step Diffusion Distillation through Score Implicit Matching](https://mlsanity.com/paper/2410.16794/) (2024)
- [Diff-Instruct++: Training One-step Text-to-image Generator Model to Align with Human Preferences](https://mlsanity.com/paper/2410.18881/) (2024)
- [Schedule On the Fly: Diffusion Time Prediction for Faster and Better Image Generation](https://mlsanity.com/paper/2412.01243/) (2024)
- [Flow Generator Matching](https://mlsanity.com/paper/2410.19310/) (2024)
- [Self-Guidance: Boosting Flow and Diffusion Generation on Their Own](https://mlsanity.com/paper/2412.05827/) (2024)
- [How much is a noisy image worth? Data Scaling Laws for Ambient Diffusion](https://mlsanity.com/paper/2411.02780/) (2024)
- [Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusion](https://mlsanity.com/paper/2502.21278/) (2025)
- [David and Goliath: Small One-step Model Beats Large Diffusion with Score Post-training](https://mlsanity.com/paper/2410.20898/) (2024)
- [InstantViR: Real-Time Video Inverse Problem Solver with Distilled Diffusion Prior](https://mlsanity.com/paper/2511.14208/) (2025)
- [Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey](https://mlsanity.com/paper/2510.14114/) (2025)
- [Unbiased Diffusion Variational Inversion via Principled Posterior Matching](https://mlsanity.com/paper/2605.25042/) (2026)

## Abstract (arXiv)

Diffusion models (DMs) have emerged as powerful generative models for solving inverse problems, offering a good approximation of prior distributions of real-world image data. Typically, diffusion models rely on large-scale clean signals to accurately learn the score functions of ground truth clean image distributions. However, such a requirement for large amounts of clean data is often impractical in real-world applications, especially in fields where data samples are expensive to obtain. To address this limitation, in this work, we introduce FlowDiff, a novel joint training paradigm that leverages a conditional normalizing flow model to facilitate the training of diffusion models on corrupted data sources. The conditional normalizing flow try to learn to recover clean images through a novel amortized inference mechanism, and can thus effectively facilitate the diffusion model's training with corrupted data. On the other side, diffusion models provide strong priors which in turn improve the quality of image recovery. The flow model and the diffusion model can therefore promote each other and demonstrate strong empirical performances. Our elaborate experiment shows that FlowDiff can effectively learn clean distributions across a wide range of corrupted data sources, such as noisy and blurry images. It consistently outperforms existing baselines with significant margins under identical conditions. Additionally, we also study the learned diffusion prior, observing its superior performance in downstream computational imaging tasks, including inpainting, denoising, and deblurring.