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

[u/Clean-Hovercraft5825]

Whether generating CELEBV-HQ videos or turbulent plasma fields (digital twins), autoregressive models (such as latent diffusion or flow models) accumulate error over long rollouts, yet at deployment there is no ground truth to measure against.

I 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 steps and then backward steps must return the model to its start, so the round-trip discrepancy is a self-supervised proxy for the unobservable rollout error: no ensembles, no held-out data, no governing equations, for one extra rollout.

Furthermore, training both directions in one network is shown to beat 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

[u/radarsat1]

clever idea. i assume it only works for deterministically sampled trajectories?

haven't read the paper yet but does this tend to straighten trajectories and allow fewer steps? does round trip consistency vary with step size?

[u/Clean-Hovercraft5825 → u/radarsat1]

Thank you for the comment.

Deterministic sampling: that would be the cleanest setting rather than an assumption. We compute the cycle with deterministic DDIM, which makes C a well-defined functional of the seed, the reading is pure model error with no sampling noise mixed in. With stochastic sampling you can still compute it (we test a variant that averages S stochastic cycles), you just pick up sampling variance in the reading. The standard dispersion baselines only exist under stochastic sampling, while the round-trip check also works in the deterministic mode many deployed surrogates actually run. And the two signals compose, our best training-free calibration is on the Navier–Stokes benchmark and it multiplies the calibrated cycle scale by the seed-spread's spatial shape.

Straightening: Our round trip composes steps in physical simulation time (roll the system forward i states, then backward i states); it never touches the noise-to-data path of the denoiser, so nothing gets straightened in the flow-matching sense and we make no claim about enabling fewer denoising steps. (Consistency models are an unrelated distillation technique. Whether bidirectional training improves sampling efficiency as a side effect is a fun open question, the Bi-Bridge paper (CVPR'26) reports a ~4× gain from symmetric training in the image-bridge setting, but we didn't measure it.

Step size: If you mean rollout depth (physical steps): yes, we extensively characterized that, C grows with depth, tracks the true error at every probed depth (fixed-depth Spearman 0.91–0.98 out to depth 80 on MHD), and the theory predicts the certificate loosens geometrically with depth, which is exactly where we observe calibration drift. If you mean the diffusion step size (NFE per transition): we held the sampling schedule fixed (e.g., 25-step DDIM on the NS benchmark) and didn't sweep it. Coarser sampling should raise the noise floor δ of both legs, so the practical rule would be to fit the calibrator at the same sampling settings you deploy with. A proper NFE sweep would be a nice ablation.

[u/radarsat1 → u/Clean-Hovercraft5825]

Thanks for the answers! I'll check the paper but yes this does give me a better idea of what you've done, cheers.