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

The Core Problem and Solution

Autoregressive models—which predict one step at a time by feeding their own outputs back as inputs—suffer from error accumulation during long predictions. Once deployed, you can't measure how wrong the model is getting because there's no ground truth to compare against. This paper presents an elegant self-checking mechanism: train a single bidirectional diffusion model that can step a dynamical system (like fluid flows or videos) either forward or backward in time. At test time, rolling forward i steps and then backward i steps should return you to the starting point. The gap between where you end up and where you started—the "round-trip discrepancy"—directly measures rollout error without needing ensembles, held-out validation data, or knowledge of the underlying physics equations.

How It Works

The authors use a conditional latent diffusion model with a direction flag: the same neural network learns to predict the next state in either temporal direction. This is not two separate models—it's one model that learns both directions simultaneously and actually performs better in both directions than direction-specific specialists.

The key insight is that round-trip consistency is free. You pay for one extra forward-and-backward rollout to get an error signal, and that's it. No ensemble overhead. At deployment, after predicting i steps forward, you can optionally run the model backward i steps. The mismatch C_i becomes your error proxy.

To use this signal practically, the authors fit a simple calibration function on training rollouts: given C_i and rollout depth, predict the actual error magnitude. This calibrator transfers to held-out test trajectories.

Validation and Impact

On compressible magnetohydrodynamics (a complex astrophysical simulation), the round-trip discrepancy ranks actual rollout errors with Spearman correlation 0.91–0.98 at fixed depth. A fitted calibrator predicts error magnitude to within 1.14× (at 68% coverage) and 1.29× (at 95% coverage)—barely one "nat" (information unit) worse than a depth-only baseline, despite being entirely self-supervised.

The method also flags out-of-distribution inputs. On the Orszag-Tang vortex (a known challenging case where sampling-dispersion baselines fail), round-trip consistency achieves 0.98 AUROC and can reduce incurred error by 15% at 80% coverage—three times better than depth-only flagging.

On the LE-PDE-UQ turbulent Navier-Stokes benchmark, a single bidirectional model matches the accuracy of a ten-model ensemble at one-tenth the training cost, with the best training-free pixel-level confidence calibration reported.

The backward direction doubles as a fast inverse solver, providing additional practical utility beyond error measurement.

Why This Matters

Most error estimation requires either ensemble diversity (computationally expensive) or held-out validation data (information leakage). Round-trip consistency exploits reversibility—a structural property of the problem domain—to create a measurement-free error signal at nearly zero cost. For high-stakes scientific computing (climate, astrophysics, turbulence), knowing when your model is drifting is essential. This approach makes that possible at deployment time for any reversible system.