模型感知调度通过纤维最优传输改进生成
Model-Aware Schedules Improve Generation via Fiberwise Optimal Transport
- Arnold-Sommerfeld-Center for Theoretical Physics（阿诺德-索末菲理论物理中心）
- Ludwig-Maximilians-Universität München（慕尼黑大学）
- Institute of Informatics, Ludwig-Maximilians-Universität München（慕尼黑大学信息学研究所）
- Munich Center for Machine Learning（慕尼黑机器学习中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出基于纤维最优传输的模型感知调度方法，通过结合预测风险与动力学作用优化时间分配，在扩散和流匹配模型中持续优于基线，显著降低FID。
AI中文摘要：
扩散和流匹配调度控制信号和噪声系数，这些系数沿仿射概率路径混合数据和噪声。最小化由最优传输启发的、定义在系数路径上的动力学作用，有助于解释强基线，但仍是模型无关的，并忽略预测误差。这里我们引入一种基于纤维最优传输的模型感知调度构建。在概率路径上的固定时间和状态处，兼容的信号/噪声分解形成一个仿射纤维。我们通过在这些纤维内平均真实分解与预测器诱导分解之间的最优传输成本来定义纤维预测风险。在固定系数曲线上，将此风险与系数路径动力学作用相结合，产生闭式最优时间分配。该构建扩展到一般线性预测目标，且风险概况可从早期基线检查点估计。我们评估了DDPM和流匹配在不同预测目标、训练配置、风险估计检查点、数据集和架构上的表现。我们的模型感知调度持续优于强基线，包括在CIFAR-10上16次函数评估时流匹配的相对FID降低38.6%。每个模型无关的动力学基线确定其自身的动力学参考坐标。在这些坐标中，来自不同设置下独立训练模型的纤维风险概况在归一化到单位面积后紧密对齐。训练中使用的所得调度变形也对齐，表明在评估的模型和设置中具有经验普遍性。预训练检查点诊断将此归一化风险一致性扩展到更大的条件潜扩散和2-RF模型。冻结的解析分配模板保留了大部分模型感知改进，而无需进一步的风险估计或模型特定拟合。
英文摘要：
Diffusion and flow-matching schedules control the signal and noise coefficients that mix data and noise along affine probability paths. Minimizing a kinetic action defined on coefficient paths, motivated by optimal transport, helps explain strong baselines but remains model-agnostic and ignores prediction error. Here we introduce a model-aware schedule construction based on fiberwise optimal transport. At a fixed time and state on the probability path, compatible signal/noise decompositions form an affine fiber. We define a fiberwise prediction risk by averaging optimal-transport costs between the true and predictor-induced decompositions within these fibers. On a fixed coefficient curve, combining this risk with coefficient-path kinetic action yields a closed-form optimal time allocation. This construction extends to general linear prediction targets, and the risk profile can be estimated from an early baseline checkpoint. We evaluate DDPMs and flow matching across prediction targets, training configurations, risk-estimation checkpoints, datasets, and architectures. Our model-aware schedules consistently outperform strong baselines, including a 38.6% relative FID reduction for flow matching on CIFAR-10 at 16 function evaluations. Each model-agnostic kinetic baseline determines its own kinetic reference coordinate. In these coordinates, fiberwise-risk profiles from independently trained models in different settings align closely after normalization to unit area. The resulting schedule deformations used in training also align, suggesting empirical universality across the evaluated models and settings. Pretrained-checkpoint diagnostics extend this normalized-risk agreement to larger conditional latent diffusion and 2-RF models. A frozen analytic allocation template retains most of the model-aware improvement without further risk estimation or model-specific fitting.
