Asymptotically Exact Negative Guidance of Diffusion Models via Positive-Unlabeled Learning

Hirohane Takagi, Masashi Sugiyama

Negative guidance of diffusion models generates samples that avoid an undesired condition, specified either by reference samples or by a conditional score alongside an unconditional model. Existing methods inject repulsive terms derived from local information at each sample, so the resulting sampler does not target an explicit density, and its bias cannot be systematically reduced by increasing computation. We instead present a negative-guidance method that samples from an explicit target density, which uniformly handles both reference-sample and score-based specifications and suppresses probability mass near the undesired condition with an avoidance strength that parametrizes the target density itself. Realizing this target requires estimating, at each diffusion timestep, how likely each sample is to belong to the undesired condition. We cast this estimation as a Positive-Unlabeled learning problem that admits lightweight online training along the diffusion trajectory, using condition samples as positives and diffusion particles as unlabeled data. Because the guided particles drift from the unconditional marginal, we further correct the residual mismatch via Sequential Monte…