# Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inference

arXiv: https://arxiv.org/abs/2602.07102 · HTML: https://mlsanity.com/paper/2602.07102/

## Key facts

- Cited by 1 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 30 of its 42 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [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)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Rethinking FID: Towards a Better Evaluation Metric for Image Generation](https://mlsanity.com/paper/2401.09603/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Scalable High-Resolution Pixel-Space Image Synthesis with Hourglass Diffusion Transformers](https://mlsanity.com/paper/2401.11605/) (2024)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Variational Diffusion Posterior Sampling with Midpoint Guidance](https://mlsanity.com/paper/2410.09945/) (2024)
- [A Mixture-Based Framework for Guiding Diffusion Models](https://mlsanity.com/paper/2502.03332/) (2025)
- [Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior](https://mlsanity.com/paper/2309.01949/) (2023)
- [LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimization](https://mlsanity.com/paper/2503.12615/) (2025)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems](https://mlsanity.com/paper/2407.16125/) (2024)
- [InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems](https://mlsanity.com/paper/2504.01689/) (2025)
- [Learning few-step posterior samplers by unfolding and distillation of diffusion models](https://mlsanity.com/paper/2507.02686/) (2025)

## Built on by (most cited first, 1 of 1)

- [Consistency Regularised Gradient Flows for Inverse Problems](https://mlsanity.com/paper/2605.07907/) (2026)

## Abstract (arXiv)

Zero-shot diffusion posterior sampling offers a flexible framework for inverse problems by accommodating arbitrary degradation operators at test time, but incurs high computational cost due to repeated likelihood-guided updates. In contrast, previous amortized diffusion approaches enable fast inference by replacing likelihood-based sampling with implicit inference models, but at the expense of robustness to unseen degradations. We introduce an amortization strategy for diffusion posterior sampling that preserves explicit likelihood guidance by amortizing the inner optimization problems arising in variational diffusion posterior sampling. This accelerates inference for in-distribution degradations while maintaining robustness to previously unseen operators, thereby improving the trade-off between efficiency and flexibility in diffusion-based inverse problems.