# WeightFlow: Learning Stochastic Dynamics via Evolving Weight of Neural Network

arXiv: https://arxiv.org/abs/2508.00451 · HTML: https://mlsanity.com/paper/2508.00451/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2025.

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

- [Tracking large chemical reaction networks and rare events by neural networks](https://mlsanity.com/paper/2512.10309/) (2025)
- [You Only Need Minimal RLVR Training: Extrapolating LLMs via Rank-1 Trajectories](https://mlsanity.com/paper/2605.21468/) (2026)
- [Render, Don't Decode: Weight-Space World Models with Latent Structural Disentanglement](https://mlsanity.com/paper/2605.06298/) (2026)
- [Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions](https://mlsanity.com/paper/2608.25606/) (2026)

## Abstract (arXiv)

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.