# Diffusion-PINN Sampler

arXiv: https://arxiv.org/abs/2410.15336 · HTML: https://mlsanity.com/paper/2410.15336/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 20 Oct 2024.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [Denoising Diffusion Samplers](https://mlsanity.com/paper/2302.13834/) (2023)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [Learning Interpolations between Boltzmann Densities](https://mlsanity.com/paper/2301.07388/) (2023)
- [Blindness of score-based methods to isolated components and mixing proportions](https://mlsanity.com/paper/2008.10087/) (2020)
- [Stochastic Localization via Iterative Posterior Sampling](https://mlsanity.com/paper/2402.10758/) (2024)
- [Liouville Flow Importance Sampler](https://mlsanity.com/paper/2405.06672/) (2024)
- [Closing the ODE-SDE gap in score-based diffusion models through the Fokker-Planck equation](https://mlsanity.com/paper/2311.15996/) (2023)

## Built on by (most cited first, 7 of 7)

- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control](https://mlsanity.com/paper/2508.10684/) (2025)
- [Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching](https://mlsanity.com/paper/2603.00530/) (2026)
- [Diffusion-based Annealed Boltzmann Generators : benefits, pitfalls and hopes](https://mlsanity.com/paper/2601.21026/) (2026)
- [PILD: Physics-Informed Learning via Diffusion](https://mlsanity.com/paper/2601.21284/) (2026)
- [Value Gradient Sampler: Learning Invariant Value Functions for Equivariant Diffusion Sampling](https://mlsanity.com/paper/2502.13280/) (2025)
- [Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling](https://mlsanity.com/paper/2607.06841/) (2026)

## Abstract (arXiv)

Recent success of diffusion models has inspired a surge of interest in developing sampling techniques using reverse diffusion processes. However, accurately estimating the drift term in the reverse stochastic differential equation (SDE) solely from the unnormalized target density poses significant challenges, hindering existing methods from achieving state-of-the-art performance. In this paper, we introduce the Diffusion-PINN Sampler (DPS), a novel diffusion-based sampling algorithm that estimates the drift term by solving the governing partial differential equation of the log-density of the underlying SDE marginals via physics-informed neural networks (PINN). We prove that the error of log-density approximation can be controlled by the PINN residual loss, enabling us to establish convergence guarantees of DPS. Experiments on a variety of sampling tasks demonstrate the effectiveness of our approach, particularly in accurately identifying mixing proportions when the target contains isolated components.