We present DistillKac, a fast image generator that uses the damped wave equation and its stochastic Kac representation to move probability mass at finite speed. In contrast to diffusion models whose reverse time velocities can become stiff and implicitly allow unbounded propagation speed, Kac dynamics enforce finite speed transport and yield globally bounded kinetic energy. Building on this structure, we introduce classifier-free guidance in velocity space that preserves square integrability under mild conditions. We then propose endpoint only distillation that trains a student to match a frozen teacher over long intervals. We prove a stability result that promotes supervision at the endpoints to closeness along the entire path. Experiments demonstrate DistillKac delivers high quality samples with very few function evaluations while retaining the numerical stability benefits of finite speed probability flows.

翻译：本文提出DistillKac，一种基于阻尼波动方程及其随机Kac表示、以有限速度移动概率质量的快速图像生成器。与扩散模型中反向时间速度可能变得刚性并隐式允许无限传播速度不同，Kac动力学强制有限速度传输并产生全局有界的动能。基于此结构，我们在速度空间中引入满足温和条件下平方可积性的无分类器引导。随后提出仅端点蒸馏方法，训练学生模型在长区间内匹配冻结的教师模型。我们证明了稳定性结果，表明端点处的监督能促进整个路径上的逼近性。实验表明，DistillKac能以极少的函数评估次数生成高质量样本，同时保持有限速度概率流的数值稳定性优势。