往返一致性：双向扩散模型能够预测其自身的展开误差

摘要

自回归模型在长程推演中会累积误差，但在部署时却没有可用于衡量该误差的真值。我们训练了一个条件潜扩散模型，它通过一个方向标志使动力系统在时间上向前或向后演化。我们表明，这种双向性提供了一种无需测量的测试时误差信号：前向推演i步再后向推演i步必须使模型返回起点，因此往返差异C_i是作为不可观测推演误差的自监督代理指标：无需集成、无需留出数据、无需控制方程，只需额外一次推演。我们在可压缩磁流体动力学(MHD)、天体物理湍流辐射混合层以及自然人脸视频(CelebV-HQ)上进行了验证。在留出的MHD轨迹上，C_i对推演误差进行排序（固定深度下斯皮尔曼相关系数为0.91–0.98；轨迹内为0.69±0.16），并且一个在训练推演上拟合的简单校准器能在接近标称覆盖率下，将其幅度预测在1.14倍（68%）和1.29倍（95%）以内——比仅基于深度的预测器多出一个nat，并可迁移到全部六个解码物理场。相同的信号在采样分散基线失效的地方，精确地标示出分布外的Orszag–Tang涡旋（AUROC 0.98；至深度10时达到1.0），并在80%覆盖率下将所产生的误差降低15%——是仅基于深度基线的三倍。双向训练的成本为负，在两个方向上都胜过单项方向专家，并且后向方向还可兼作快速逆向求解器。在LE-PDE-UQ的湍流Navier–Stokes基准上，一个双向模型仅以十分之一的训练成本，就达到了其十模型集成1.3倍以内的精度，并具有最佳的免训练像素级校准。往返一致性将可逆性转化为生成模型的实用信任信号。

English

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 C_i 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, C_i ranks rollout error (Spearman 0.91-0.98 at fixed depth; 0.69 pm 0.16 within trajectories), and a simple calibrator fit on training rollouts predicts its magnitude to within 1.14times (68%) and 1.29times (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 1.3times 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.