Asymptotically Exact Negative Guidance of Diffusion Models via Positive-Unlabeled Learning
Negative guidance in diffusion models aims to steer generation away from undesired conditions, but existing methods rely on local repulsive terms that do not target an explicit density and whose bias cannot be reduced by more computation. This paper recasts the problem as sampling from the explicit avoidance density $p_{\text{target}}(x) \propto p(x)(1-p(c \mid x))^{\lambda}$, estimates the per-timestep posterior $p_t(c \mid x_t)$ via online Positive-Unlabeled learning, and corrects particle drift with Sequential Monte Carlo. The result is a principled sampler that is asymptotically exact in the particle limit and empirically Pareto-dominates existing methods on avoidance-quality trade-offs across Gaussian mixtures, CIFAR-10, and Stable Diffusion.
The paper successfully formalizes a previously heuristic area of diffusion guidance by introducing an explicit target density and an asymptotically exact SMC sampler. Its core insight—casting the posterior estimation problem as Positive-Unlabeled learning on running particles—is both novel and practically useful. However, the theoretical guarantee relies on an idealized auxiliary particle system rather than the single-system algorithm actually implemented, and the image-scale experiments substitute the theoretically justified uPU loss with BCE, loosening the theory-practice connection.
The explicit density formulation in Eq. (1) is conceptually sound: it replaces ad-hoc repulsion strengths with a meaningful tempering parameter $\lambda$ that directly controls avoidance. The online PU estimator is lightweight and naturally handles both reference-sample and score-based settings by importance-reweighting diffusion particles as unbiased unlabeled data. Empirically, the method is compelling: on a 3D GMM it matches the oracle in posterior leak and Wasserstein distance, while on CIFAR-10 and Stable Diffusion it Pareto-dominates the Safe Denoiser and SLD baselines when serving as their SMC proposal.
The asymptotic exactness proof (Theorem 1) analyzes a variant with an independent auxiliary particle system for training $f_t$, whereas the practical Algorithm 1 uses the same running particles for both classifier refitting and SMC estimation, breaking the independence required by the proof. The assumptions are also strong: realizability of the Bayes logit and strict two-sided non-degeneracy $\delta \leq p(c \mid x) \leq 1-\delta$ are unlikely to hold for the linear probes and kernel logistic models used in experiments. Most importantly, in the CIFAR-10 experiments the authors abandon the theoretically unbiased uPU risk for standard binary cross-entropy because the particle count is too small for uPU to be stable, which undermines the claim that the implemented method follows the derived theory exactly.
The evidence is strongest on the GMM, where closed-form ground-truth densities allow rigorous evaluation: the method simultaneously matches the oracle in posterior leak and avoids the mode collapse seen in NegCFG and the residual leakage seen in DNG. The large-scale comparisons are fair because the method uses existing guidance kernels (Safe Denoiser, SLD) as proposals, isolating the gain from the PU/SMC layer. One caveat is that the Stable Diffusion oracle floor is constructed by filtering a non-avoided pool with a learned style detector, so it is an operational reference rather than a true distributional lower bound, and the detector itself introduces uncharacterized bias.
The authors provide code and link to a GitHub repository. Experimental details are relegated to Appendix D, which does specify pretrained checkpoints, particle counts, and classifier architectures (e.g., a linear probe on pooled UNet bottleneck features for CIFAR-10). Reproduction should be feasible for the GMM and CIFAR-10 settings given standard resources, though the exact number of gradient steps per timestep for the online classifier and the ESS threshold $\text{ESS}_{\min}$ are not stated in the main text. The per-timestep refitting and adaptive resampling add nontrivial overhead that is not benchmarked against baseline runtime, which could hinder independent verification at image scale.
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 Carlo, yielding a sampler that is asymptotically exact in the particle limit and that turns any existing negative-guidance method into its proposal kernel. Empirically, our method approaches the ground-truth target on Gaussian mixtures and Pareto-dominates existing methods on trade-offs between avoidance and generation quality, distributional bias, and diversity, including in an image-generation setting with a pretrained score network.
Pick a starting point or write your own. Challenges run in the background, so you can keep reading while the AI investigates.
No challenges yet. Disagree with the review? Ask the AI to revisit a specific claim.