# Accurate Sampling from Diffusion Models

arXiv: https://arxiv.org/abs/2609.29902 · HTML: https://mlsanity.com/paper/2609.29902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 15 of 15)

- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [An Introduction to Deep Generative Modeling](https://mlsanity.com/paper/2103.05180/) (2021)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [Introduction to Normalizing Flows for Lattice Field Theory](https://mlsanity.com/paper/2101.08176/) (2021)
- [Aspects of scaling and scalability for flow-based sampling of lattice QCD](https://mlsanity.com/paper/2211.07541/) (2022)
- [Stochastic normalizing flows as non-equilibrium transformations](https://mlsanity.com/paper/2201.08862/) (2022)
- [Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows](https://mlsanity.com/paper/2110.02673/) (2021)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Understanding Diffusion Models by Feynman's Path Integral](https://mlsanity.com/paper/2403.11262/) (2024)
- [Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows](https://mlsanity.com/paper/2307.01107/) (2023)
- [On learning higher-order cumulants in diffusion models](https://mlsanity.com/paper/2410.21212/) (2024)
- [Generative models for scalar field theories: how to deal with poor scaling?](https://mlsanity.com/paper/2301.01504/) (2023)
- [AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning](https://mlsanity.com/paper/2401.15948/) (2024)
- [Combining complex Langevin dynamics with score-based and energy-based diffusion models](https://mlsanity.com/paper/2510.01328/) (2025)

## Abstract (arXiv)

A new proposal called DM-SMC (Diffusion Model - Sequential Monte Carlo) is investigated, which samples ensembles defined in terms of an action, using diffusion models trained on samples from the ensemble. The SMC setup allows for accurate sampling in spite of an approximate diffusion model and the finite stepsize used in the numerical solution of the stochastic process. Improved update strategies are also investigated. Results are presented for a Z2 symmetric scalar field theory in 2 dimensions near its 2nd order phase transition.