发表机构
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出双向扩散模型的往返偏差可作为自监督代理预测生成模型推演误差，在多类任务中验证其有效性，兼具逆求解功能且训练成本低。
AI 中文摘要
自回归模型在长序列推演过程中会累积误差，但在部署时并无真实值用于衡量该误差。我们训练了一个单一的条件潜在扩散模型，该模型可通过方向标志实现动力系统的时间正向或反向推演，并且证明这种双向性提供了一种无需额外测试的误差信号：正向推演i步后再反向推演i步，模型必须回到初始状态，因此往返偏差𝒞ᵢ可作为不可观测推演误差的自监督代理，无需集成模型、预留数据或控制方程，仅需一次额外推演即可实现。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。在预留的MHD轨迹上，𝒞ᵢ可对推演误差进行排序（固定深度时斯皮尔曼相关系数为0.91-0.98；轨迹内为0.69±0.16），对训练推演过程拟合的简单校准器可将误差幅度预测至1.14倍（68%置信度）和1.29倍（95%置信度），覆盖度接近标称值，仅比仅深度预测器差1 nat，且可迁移至所有6个解码物理场。相同信号可精准标记分布外的Orszag-Tang涡旋（AUROC为0.98；深度为10时达1.0），而采样分散基线在此处会出现反转，且在80%覆盖度下可将已产生的误差降低15%，是仅深度基线的三倍。双向训练无额外成本，在两个方向上均优于方向专用模型，且反向方向可作为快速逆求解器。在LE-PDE-UQ的湍流纳维-斯托克斯基准测试中，单一双向模型的精度达到其十模型集成的1.3倍以内，训练成本仅为十分之一，且具备最佳的无训练像素级校准能力。往返一致性将可逆性转化为生成模型的实用置信信号。
英文摘要
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 $\mathcal{C}_i$ 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, $\mathcal{C}_i$ 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 $1.14\times$ ($68\%$) and $1.29\times$ ($95\%$) 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 $1.3\times$ 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.
CommentsCode: https://github.com/alexscheinker/round-trip-consistency
