mlsanityData to 7 Oct 2026

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

arXiv 2608.00675 ↗First posted 1 Aug 2026stat.ML cs.LG physics.comp-phcited by 0

On the map: Diffusion models → Flow matching, time series and science

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.

Key facts. No citing papers in the map yet (data through 7 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.

Builds on

43 of 72 references.

Closest ancestors · 8

Same direction, newest first

  1. 2026Bidirectional Autoregressive Latent Diffusion for Forward and Inverse Magnetohydrodynamics28 Jun
  2. 2026PhaseFlow4D: Physically Constrained 4D Beam Reconstruction via Feedback-Guided Latent Diffusion4 Apr
  3. 2026DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solving14 Feb
  4. 2025Generative Latent Neural PDE Solver using Flow Matching28 Mar
  5. 2024On conditional diffusion models for PDE simulations21 Oct
  6. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation4 Sep
  7. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers10 Aug
  8. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun

Other references · 35

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  7. 2013Auto-Encoding Variational Bayescited by 3,980
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  9. 2020Taming Transformers for High-Resolution Image Synthesiscited by 3,229
  10. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  11. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,362
  12. 2017Non-local Neural Networkscited by 2,290
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  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  4. 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,274
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2017Selective Classification for Deep Neural Networkscited by 799
  7. 2024Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusioncited by 634
  8. 2021Machine learning accelerated computational fluid dynamicscited by 461
  9. 2018Accurate Uncertainties for Deep Learning Using Calibrated Regressioncited by 417
  10. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  11. 2018Invertible Residual Networkscited by 364
  12. 2019Learning Correspondence from the Cycle-Consistency of Timecited by 269
  13. 2022CelebV-HQ: A Large-Scale Video Facial Attributes Datasetcited by 246
  14. 2023Efficient Diffusion Training via Min-SNR Weighting Strategycited by 242
  15. 2017UnFlow: Unsupervised Learning of Optical Flow with a Bidirectional Census Losscited by 202
  16. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
  17. 2015The Benefit of Multitask Representation Learningcited by 194
  18. 2024The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learningcited by 134
  19. 2021Uncertainty Toolbox: an Open-Source Library for Assessing, Visualizing, and Improving Uncertainty Quantificationcited by 57
  20. 2020Time-Reversal Symmetric ODE Networkcited by 19
  21. 2023Cycle Consistency-based Uncertainty Quantification of Neural Networks in Inverse Imaging Problemscited by 4
  22. 2024Time-Reversal Provides Unsupervised Feedback to LLMscited by 3
  23. 2022Improving Motion Forecasting for Autonomous Driving with the Cycle Consistency Losscited by 1

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