# Posterior Sampling with Denoising Oracles via Tilted Transport arXiv: https://arxiv.org/abs/2407.00745 ยท HTML: https://mlsanity.com/paper/2407.00745/ ## 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 35 of its 72 references that are in the map. - First posted on arXiv 30 Jun 2024. ## 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 35) - [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) - [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015) - [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018) - [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) - [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021) - [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021) - [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021) - [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022) - [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021) - [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021) - [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023) - [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023) - [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) - [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022) - [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021) - [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022) - [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022) - [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015) - [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023) - [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023) - [Notes on Computational Hardness of Hypothesis Testing: Predictions using the Low-Degree Likelihood Ratio](https://mlsanity.com/paper/1907.11636/) (2019) - [Sampling Can Be Faster Than Optimization](https://mlsanity.com/paper/1811.08413/) (2018) - [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022) - [Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization](https://mlsanity.com/paper/2203.05093/) (2022) - [Learning general Gaussian mixtures with efficient score matching](https://mlsanity.com/paper/2404.18893/) (2024) - [Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors](https://mlsanity.com/paper/2403.11407/) (2024) ## Built on by (most cited first, 12 of 12) - [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024) - [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024) - [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025) - [Taming Diffusion Models for Image Restoration: A Review](https://mlsanity.com/paper/2409.10353/) (2024) - [Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributions](https://mlsanity.com/paper/2409.20547/) (2024) - [Posterior sampling via Langevin dynamics based on generative priors](https://mlsanity.com/paper/2410.02078/) (2024) - [Efficient Approximate Posterior Sampling with Annealed Langevin Monte Carlo](https://mlsanity.com/paper/2508.07631/) (2025) - [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026) - [HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models](https://mlsanity.com/paper/2409.09614/) (2024) - [Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models](https://mlsanity.com/paper/2506.13614/) (2025) - [Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stability](https://mlsanity.com/paper/2605.06538/) (2026) - [Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey](https://mlsanity.com/paper/2510.14114/) (2025) ## Abstract (arXiv) Score-based diffusion models have significantly advanced high-dimensional data generation across various domains, by learning a denoising oracle (or score) from datasets. From a Bayesian perspective, they offer a realistic modeling of data priors and facilitate solving inverse problems through posterior sampling. Although many heuristic methods have been developed recently for this purpose, they lack the quantitative guarantees needed in many scientific applications. In this work, we introduce the textittilted transport technique, which leverages the quadratic structure of the log-likelihood in linear inverse problems in combination with the prior denoising oracle to transform the original posterior sampling problem into a new `boosted' posterior that is provably easier to sample from. We quantify the conditions under which this boosted posterior is strongly log-concave, highlighting the dependencies on the condition number of the measurement matrix and the signal-to-noise ratio. The resulting posterior sampling scheme is shown to reach the computational threshold predicted for sampling Ising models [Kunisky'23] with a direct analysis, and is further validated on high-dimensional Gaussian mixture models and scalar field varphi4 models.