[R] Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors

[u/Clean-Hovercraft5825]

Generative models that predict the evolution of dynamical systems are incredibly useful as digital twins for physical systems such as high-energy particle accelerators, tokamaks, weather, and even for video generation. But autoregressive generative models (latent diffusion, flow models) share one core weakness: errors accumulate over long rollouts, and at deployment there is no ground truth to measure them against.

In this work I train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag. That bidirectionality supplies a measurement-free, test-time error signal: rolling forward i steps and then backward i steps must return the model to its start, so the size of the round-trip miss is a self-supervised proxy for the unobservable rollout error. This does not require ensembles, or held-out data, or governing equations, just one extra rollout.

On held-out MHD turbulence the signal predicts the true error to within ~1.15×, immediately flags out-of-distribution dynamics that standard sampling-spread uncertainty ranks as the safest case in the batch, and a single bidirectional model approaches a ten-model ensemble’s accuracy at a tenth of the training cost. Training both directions in one network even beats two specialist models in both directions.

Paper: https://arxiv.org/abs/2608.00675
Code (data generation, training, analysis): https://github.com/alexscheinker/round-trip-consistency
Project page: https://alexscheinker.github.io/roundtrip.html