AI 中文总结
本文提出FoRM方法，将关系知识迁移转化为关系流形上的流图映射问题，通过安全半群一致性约束等优化，在5项图像复原任务上降低训练方差约50%，性能优于现有蒸馏基线。
AI 中文摘要
图像复原的知识蒸馏通常将教师网络与学生网络之间的中间特征或关系矩阵对齐为静态目标，忽略了知识迁移过程的动态结构。本文提出关系流形上的流图蒸馏（FoRM），将基于关系的知识迁移重新表述为关系流形上的连续流映射问题。FoRM不回归学生与教师关系状态之间的恒定速度场，而是学习流图算子$\boldsymbol{\theta}(\boldsymbol{z}, t, s)$，给定时间$t$的当前状态，直接预测任意目标时间$s$的关系状态，从而实现更丰富的轨迹级监督。为确保所学流图的全局自洽性，引入安全半群一致性约束，利用真实桥接状态强制组合一致性，消除幻影状态误差累积。端点锚定损失进一步防止算子偏离教师目标。在超分辨率、去雨、去噪、去模糊和低光增强共5项图像复原任务上进行的大量实验表明，在多种骨干架构下，FoRM相较于最先进的蒸馏基线取得了一致的性能提升，与朴素流匹配蒸馏相比，训练方差降低约50%，同时实现了更优的复原质量。
英文摘要
Knowledge distillation for image restoration typically aligns intermediate features or relation matrices between teacher and student networks as static targets, ignoring the dynamic structure of the knowledge transfer process. In this paper, we propose Flow-Map Distillation on Relation Manifolds (FoRM), which reformulates relation-based knowledge transfer as a continuous flow mapping problem on the relation manifold. Rather than regressing a constant velocity field between student and teacher relation states, FoRM learns a flow map operator $\mathcal{F}_θ(\mathbf{z}, t, s)$ that directly predicts the relation state at any target time $s$ given the current state at time $t$, enabling richer trajectory-level supervision. To ensure global self-consistency of the learned flow map, we introduce a safe semigroup consistency constraint that enforces compositional agreement using ground-truth bridge states, eliminating phantom-state error accumulation. An endpoint anchoring loss further prevents the operator from drifting away from the teacher target. Extensive experiments on five image restoration tasks, including super-resolution, deraining, denoising, deblurring, and low-light enhancement, demonstrate consistent gains over state-of-the-art distillation baselines across multiple backbone architectures, reducing training variance by approximately 50\% compared to naive flow matching distillation while achieving superior restoration quality.
Comments9 pages, 7 figures. Accepted to ACM Multimedia 2026
