[2512.01153] DPAC: Distribution-Preserving Adversarial Control for Diffusion Sampling

Computer Science > Computer Vision and Pattern Recognition arXiv:2512.01153 (cs) [Submitted on 1 Dec 2025 (v1), last revised 5 Mar 2026 (this version, v2)] Title:DPAC: Distribution-Preserving Adversarial Control for Diffusion Sampling Authors:Han-Jin Lee, Han-Ju Lee, Jin-Seong Kim, Seok-Hwan Choi View a PDF of the paper titled DPAC: Distribution-Preserving Adversarial Control for Diffusion Sampling, by Han-Jin Lee and Han-Ju Lee and Jin-Seong Kim and Seok-Hwan Choi View PDF HTML (experimental) Abstract:Adversarially guided diffusion sampling often achieves the target class, but sample quality degrades as deviations between the adversarially controlled and nominal trajectories accumulate. We formalize this degradation as a path-space Kullback-Leibler divergence(path-KL) between controlled and nominal (uncontrolled) diffusion processes, thereby showing via Girsanov's theorem that it exactly equals the control energy. Building on this stochastic optimal control (SOC) view, we theoretically establish that minimizing this path-KL simultaneously tightens upper bounds on both the 2-Wasserstein distance and Fréchet Inception Distance (FID), revealing a principled connection between adversarial control energy and perceptual fidelity. From a variational perspective, we derive a first-order optimality condition for the control: among all directions that yield the same classification gain, the component tangent to iso-(log-)density surfaces (i.e., orthogonal to the score) minimizes pa...