# Posterior sampling by source-space MCMC via prior-based few-step transport maps

arXiv: https://arxiv.org/abs/2610.01034 · HTML: https://mlsanity.com/paper/2610.01034/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 27 of 27)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [RL with KL penalties is better viewed as Bayesian inference](https://mlsanity.com/paper/2205.11275/) (2022)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [Flow map matching with stochastic interpolants: A mathematical framework for consistency models](https://mlsanity.com/paper/2406.07507/) (2024)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [If at First You Don't Succeed, Try, Try Again: Faithful Diffusion-based Text-to-Image Generation by Selection](https://mlsanity.com/paper/2305.13308/) (2023)
- [BayesFlow: Amortized Bayesian Workflows With Neural Networks](https://mlsanity.com/paper/2306.16015/) (2023)
- [Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors](https://mlsanity.com/paper/2107.02926/) (2021)
- [Source-Guided Flow Matching](https://mlsanity.com/paper/2508.14807/) (2025)
- [Denoising Score-Matching for Uncertainty Quantification in Inverse Problems](https://mlsanity.com/paper/2011.08698/) (2020)
- [Optimizing The Integrator Step Size for Hamiltonian Monte Carlo](https://mlsanity.com/paper/1411.6669/) (2014)
- [Bayesian Inference with Generative Adversarial Network Priors](https://mlsanity.com/paper/1907.09987/) (2019)
- [Accelerated dimension-independent adaptive Metropolis](https://mlsanity.com/paper/1506.05741/) (2015)
- [Transport map unadjusted Langevin algorithms: learning and discretizing perturbed samplers](https://mlsanity.com/paper/2302.07227/) (2023)
- [Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces](https://mlsanity.com/paper/2603.14798/) (2026)
- [On Variance Reduction in Learning Mean Flows](https://mlsanity.com/paper/2605.09235/) (2026)

## Abstract (arXiv)

Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, and pretrained generative models. The same computational problem appears in the test-time guidance task (generalized Bayes), where an explicit positive weight, e.g., an exponentiated reward, tilts an implicit prior. We develop a framework for source-space generalized Bayesian inference that combines inexpensive few-step prior transports with posterior stability guarantees. Specifically, we represent the prior using a one- or few-step improved MeanFlow (iMF) map and perform posterior sampling in its Gaussian source space. We establish Wasserstein error bounds between the exact and learned posteriors in terms of the joint population iMF and auxiliary-velocity loss, decomposed into training suboptimality and model-class approximation error. In the iMF source space, we adopt parallel tempering with preconditioned Crank-Nicolson updates and introduce a hybrid variant that incorporates split Hamiltonian Monte Carlo to improve sampling efficiency. Synthetic experiments show that the proposed framework can approximate posterior distributions accurately and efficiently, while CLIP-guided ImageNet experiments demonstrate its ability to steer a pretrained iMF image prior toward text-specified preferences.