# Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errors

arXiv: https://arxiv.org/abs/2608.00675 · HTML: https://mlsanity.com/paper/2608.00675/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 43 of its 72 references that are in the map.
- First posted on arXiv 1 Aug 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, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Learning Correspondence from the Cycle-Consistency of Time](https://mlsanity.com/paper/1903.07593/) (2019)
- [CelebV-HQ: A Large-Scale Video Facial Attributes Dataset](https://mlsanity.com/paper/2207.12393/) (2022)
- [Efficient Diffusion Training via Min-SNR Weighting Strategy](https://mlsanity.com/paper/2303.09556/) (2023)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [UnFlow: Unsupervised Learning of Optical Flow with a Bidirectional Census Loss](https://mlsanity.com/paper/1711.07837/) (2017)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)

## Abstract (arXiv)

Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against. We train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag, and show that this 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 round-trip discrepancy Ci is a self-supervised proxy for the unobservable rollout error: no ensembles, no held-out data, no governing equations, for one extra rollout. We validate on compressible magnetohydrodynamics (MHD), an astrophysical turbulent radiative mixing layer, and natural face videos (CelebV-HQ). On held-out MHD trajectories, Ci ranks rollout error (Spearman 0.91-0.98 at fixed depth; 0.69 ± 0.16 within trajectories), and a simple calibrator fit on training rollouts predicts its magnitude to within 1.14× (68%) and 1.29× (95%) with near-nominal coverage - one nat beyond a depth-only predictor, transferring to all six decoded physical fields. The same signal flags the out-of-distribution Orszag-Tang vortex (AUROC 0.98; 1.0 by depth 10) exactly where sampling-dispersion baselines invert, and it cuts incurred error by 15% at 80% coverage - three times the depth-only baseline. Bidirectional training comes at negative cost, beating direction specialists in both directions, and the backward direction doubles as a fast inverse solver. On LE-PDE-UQ's turbulent Navier-Stokes benchmark, a single bidirectional model reaches accuracy within 1.3× of their ten-model ensemble at a tenth of the training cost, with the best training-free pixel-level calibration. Round-trip consistency turns reversibility into a practical trust signal for generative models.