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

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Guidance for conditional diffusion

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Proposes PU Steering: negative guidance of diffusion models as sampling from an explicit avoidance density p(x)(1-p(c|x))^λ, using an online PU classifier plus SMC, asymptotically exact in the particle limit.

Problem

Existing negative guidance methods for diffusion models use local per-sample repulsion, so the sampler does not target an explicit density and its bias cannot be systematically reduced with more computation.

Approach

Cast estimation of the avoided-condition posterior p_t(c|x_t) as online Positive-Unlabeled learning (condition samples as positives, diffusion particles as unlabeled), correct particle-distribution mismatch via importance weights, and run tempered SMC with any existing negative-guidance method as proposal kernel, yielding asymptotic exactness for the avoidance target.

Key results

• On the 3D GMM (50 trials), the method matches the Oracle's posterior leak (0.012) with W2 1.8±0.6 vs Oracle 1.5±0.3, while NegCFG and DNG trade off leak against W2.
• On CIFAR-10 avoidance, the SMC layer on top of the Safe Denoiser Pareto-dominates the Safe Denoiser at the same η on FID and KL across the operating range.
• On Stable Diffusion v1.4 Van Gogh avoidance, the method at M=128, λ=16 reaches avoided-style rate 0.235 (oracle floor 0.238) with FID 28.10, beating SLD and DNG.

Surprising findings

• On CIFAR-10 the method uses binary cross-entropy in place of the uPU loss, treating references as positives and SMC particles as soft negatives, because the PU assumptions are impractical at this scale.

Limitations

• Experiments limited to low-dimensional GMM and image-scale settings; broader applications left open.
• Weight degeneracy in SMC and dependence of weight variance on online classifier inaccuracies not analyzed.
• Online PU classifier stabilization (limited positives, overfitting) left for future work.

Experimental setup

Datasets: CIFAR-10 Gaussian mixture (synthetic)

Benchmarks: CIFAR-10 Gaussian mixture W2 and posterior leak Stable Diffusion Van Gogh style avoidance

Metrics: FID KL divergence LPIPS target-class rate posterior leak 2-Wasserstein distance KID avoided-style rate

Baselines: NegCFG DNG Safe Denoiser SLD Oracle sampler

Builds on: Dynamic Negative Guidance Safe Denoiser Diffusion Alignment as Sampling (DAS) uPU learning classifier-free guidance

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