# Micro-Macro Consistency in Multiscale Modeling: Score-Based Model Assisted Sampling of Fast/Slow Dynamical Systems

arXiv: https://arxiv.org/abs/2312.05715 · HTML: https://mlsanity.com/paper/2312.05715/

## Key facts

- Cited by 4 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 32 references that are in the map.
- First posted on arXiv 10 Dec 2023.

## Placed in

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

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

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [Molecular Latent Space Simulators](https://mlsanity.com/paper/2007.00728/) (2020)
- [Chasing Collective Variables using Autoencoders and biased trajectories](https://mlsanity.com/paper/2104.11061/) (2021)
- [Score-Based Generative Models for Molecule Generation](https://mlsanity.com/paper/2203.04698/) (2022)
- [GANs and Closures: Micro-Macro Consistency in Multiscale Modeling](https://mlsanity.com/paper/2208.10715/) (2022)

## Built on by (most cited first, 4 of 4)

- [Generative Learning for Slow Manifolds and Bifurcation Diagrams](https://mlsanity.com/paper/2504.20375/) (2025)
- [Enabling Probabilistic Learning on Manifolds through Double Diffusion Maps](https://mlsanity.com/paper/2506.02254/) (2025)
- [A Multimodal Conditional Mixture Model with Distribution-Level Physics Priors](https://mlsanity.com/paper/2602.10451/) (2026)
- [Generative Learning of Separatrices](https://mlsanity.com/paper/2608.14743/) (2026)

## Abstract (arXiv)

A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of the phase space over long timescales of interest; this task is not, however, without challenges. For example, the long term behavior of a system with many degrees of freedom often cannot be efficiently computationally explored by direct dynamical simulation; such systems can often become trapped in local free energy minima. In the study of physics-based multi-time-scale dynamical systems, techniques have been developed for enhancing sampling in order to accelerate exploration beyond free energy barriers. On the other hand, in the field of Machine Learning, a generic goal of generative models is to sample from a target density, after training on empirical samples from this density. Score based generative models (SGMs) have demonstrated state-of-the-art capabilities in generating plausible data from target training distributions. Conditional implementations of such generative models have been shown to exhibit significant parallels with long-established -- and physics based -- solutions to enhanced sampling. These physics-based methods can then be enhanced through coupling with the ML generative models, complementing the strengths and mitigating the weaknesses of each technique. In this work, we show that that SGMs can be used in such a coupling framework to improve sampling in multiscale dynamical systems.