# PINGS: Physics-Informed Neural Network for Fast Generative Sampling

arXiv: https://arxiv.org/abs/2509.11284 · HTML: https://mlsanity.com/paper/2509.11284/

## 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 9 of its 17 references that are in the map.
- First posted on arXiv 14 Sep 2025.

## Placed in

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

## Builds on (most cited first, 9 of 9)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)

## Abstract (arXiv)

We introduce PINGS (Physics-Informed Neural Network for Fast Generative Sampling), a framework that amortizes diffusion sampling by training a physics-informed network to approximate reverse-time probability-flow dynamics, reducing sampling to a single forward pass (NFE = 1). As a proof of concept, we learn a direct map from a 3D standard normal to a non-Gaussian Gaussian Mixture Model (GMM). PINGS preserves the target's distributional structure (multi-bandwidth kernel MMD2 = 1.88 × 10-2 with small errors in mean, covariance, skewness, and excess kurtosis) and achieves constant-time generation: 104 samples in 16.54 ± 0.56 millisecond on an RTX 3090, versus 468-843 millisecond for DPM-Solver (10/20) and 960 millisecond for DDIM (50) under matched conditions. We also sanity-check the PINN/automatic-differentiation pipeline on a damped harmonic oscillator, obtaining MSEs down to O(10-5). Compared to fast but iterative ODE solvers and direct-map families (Flow, Rectified-Flow, Consistency), PINGS frames generative sampling as a PINN-style residual problem with endpoint anchoring, yielding a white-box, differentiable map with NFE = 1. These proof-of-concept results position PINGS as a promising route to fast, function-based generative sampling with potential extensions to scientific simulation (e.g., fast calorimetry).