# Bidirectional Autoregressive Latent Diffusion for Forward and Inverse Magnetohydrodynamics

arXiv: https://arxiv.org/abs/2606.29620 · HTML: https://mlsanity.com/paper/2606.29620/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Improved Robustness of Deep Reinforcement Learning for Control of Time-Varying Systems by Bounded Extremum Seeking](https://mlsanity.com/paper/2510.02490/) (2025)
- [Physics-constrained 3D Convolutional Neural Networks for Electrodynamics](https://mlsanity.com/paper/2301.13715/) (2023)
- [PhaseFlow4D: Physically Constrained 4D Beam Reconstruction via Feedback-Guided Latent Diffusion](https://mlsanity.com/paper/2604.03885/) (2026)
- [Posterior Mean Matching: Generative Modeling through Online Bayesian Inference](https://mlsanity.com/paper/2412.13286/) (2024)
- [Planning for Change: Reinforcement Learning Combined with Bounded Extremum Seeking for Robotic Control under Distribution Shift](https://mlsanity.com/paper/2604.01142/) (2026)
- [Mahalanobis-Guided Latent OOD Detection for Hybrid ES-DRL Control in Time-Varying Systems](https://mlsanity.com/paper/2606.11474/) (2026)

## Built on by (most cited first, 1 of 1)

- [Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors](https://mlsanity.com/paper/2608.00675/) (2026)

## Abstract (arXiv)

This work presents a new bidirectional autoregressive latent diffusion approach for predicting the evolution of multiple fields (mass density, pressure, velocity, and magnetic field components) for magnetohydrodynamics. We show that this bidirectional flow can be used as a self-supervised consistency metric for uncertainty and error estimation, which enables the model to estimate test-time uncertainty and error without access to ground truth, by comparing how closely flowing forwards and backwards in time returns to the same predicted fields. We also demonstrate this methods's potential to serve as a non-invasive plasma diagnostic, and show how adaptive feedback can be used to make the model more robust based on sparse diagnostics or limited views/measurements.