用阻尼波动方程实现快速图像生成，速度有限且稳定
DistillKac: Few-Step Image Generation via Damped Wave Equations
- 基于阻尼波动方程的有限速度概率流
- 仅需少量函数求值即可生成高质量图像
- 适合追求高效与数值稳定的生成任务
我们提出 DistillKac，一种基于阻尼波方程及其随机 Kac 表示的快速图像生成方法，通过有限速度传输概率质量。与反向时间速度易发僵硬、隐含无限传播速度的扩散模型不同，Kac 动力学强制有限速度传输并保证全局有界动能。在此基础上，我们在速度空间引入无分类器引导，在温和条件下保持平方可积性。进一步提出仅在端点进行蒸馏的方法，训练学生模型在长区间内匹配冻结教师模型。我们证明了稳定性结果，表明端点监督可促进整个路径的接近性。实验表明，DistillKac 在极少函数求值下仍能生成高质量样本，同时保持有限速度概率流的数值稳定性优势。
原文摘要 · Abstract (English)
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.
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