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Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraints
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Proposes a zero-shot method that steers a pre-trained unconditional score-based diffusion model with a differentiable neuro-symbolic (log-probabilistic logic) soft constraint so it approximates the true conditional distribution under arbitrary logical constraints, without retraining.
Problem
Conditional sampling from score-based diffusion models under user-specified logical constraints normally requires constraint-specific training or noise-dependent classifiers, and existing zero-shot guidance methods aim at valid samples rather than the correct conditional distribution.
Approach
Modify the learned score by adding the gradient of a differentiable soft constraint weighted by a time-dependent g(t) (g(0)=1, g(1)=0), add Langevin MCMC correction at t≈0, and encode logical formulas with a log-probabilistic logic whose disjunction is a numerically stable log-probabilistic sum.
Key results
- On white wine with a complex constraint, average l1 histogram distance to rejection sampling was about 0.1 (max 0.15) versus 0.29 (max 0.85) for Universal Guidance, while constraint satisfaction was about 86% vs 92% for rejection sampling.
- On the white wine constraint, RS acceptance rate was about 1.67% whereas the method samples efficiently from low-probability regions.
- On eSIRS bridging, average l1 histogram distance was 0.13 (max 0.25) for the method vs 0.47 (max 1.0) for Universal Guidance; the inequality I(t)<=20 was met in 99% of samples.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use constraint guidance instead of Universal Guidance | White wine conditional generation · White wine | Avg L1: 0.29 vs 0.1 | Helped |
| Use constraint guidance instead of Universal Guidance | eSIRS bridging conditional generation · eSIRS bridging | Avg L1: 0.47 vs 0.13 | Helped |
| Add forward universal guidance (ablation) | DSM constraint guidance · White wine | Average L1 HD: 0.1 -> 0.123 | No clear effect |
| Add forward universal guidance (ablation) | DSM constraint guidance · eSIRS bridging | Average L1 HD: 0.152 -> 0.113 | Helped |
| Add backward universal guidance after forward universal guidance (ablation) | DSM constraint guidance · White wine | Average L1 HD: 0.123 -> 0.238 | Hurt |
| Add backward universal guidance after forward universal guidance (ablation) | DSM constraint guidance · eSIRS bridging | Average L1 HD: 0.113 -> 0.197 | Hurt |
| Add per-step self-recurrence to forward and backward universal guidance (ablation) | DSM constraint guidance · White wine | Average L1 HD: 0.238 -> 0.288 | Hurt |
| Add per-step self-recurrence to forward and backward universal guidance (ablation) | DSM constraint guidance · eSIRS bridging | Average L1 HD: 0.197 -> 0.467 | Hurt |
| Add Langevin MCMC correction to backward universal guidance (ablation) | Universal Guidance on white wine · White wine | Average L1 HD: 0.238 -> 0.141 | Helped |
| Use forward universal guidance for digit-sum conditioning (ablation) | MNIST pair generation · MNIST digits sum | constraint satisfaction: 96% -> 100% | Helped |
| Use forward universal guidance for digit-sum conditioning (ablation) | MNIST pair generation · MNIST digits sum | invalid digits: ≈ 12% -> ≈ 8% | Helped |
Surprising findings
- Universal Guidance, the state-of-the-art plug-and-play image method, produced large biases in marginals when used to model conditional distributions for tabular and time-series data.
- Backward universal guidance and self-recurrence significantly worsened distribution fidelity on tabular and time-series tasks.
Limitations
- Constraint strength must be hand-tuned, trading off constraint satisfaction against sample quality, especially for images.
- Approximation is not exact; the time-dependent weighting g(t) is heuristic and the true conditional score is only approximated for t>0.
- Image results are evaluated only visually; no quantitative metric of conditional fidelity for images.
Experimental setup
Datasets: UCI White Wine Quality UCI Adult eSIRS simulated trajectories MNIST CelebA
Benchmarks: UCI White Wine constrained marginals UCI Adult constrained generation eSIRS bridging and inequality constraints MNIST digits sum CelebA restoration and color conditioning
Metrics: l1 histogram distance average l1 correlation difference constraint satisfaction rate acceptance rate of rejection sampling
Baselines: rejection sampling Universal Guidance
Builds on: score-based generative models (SDE) Universal Guidance Logic Tensor Networks LogLTN
Closest papers by meaning
- Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers (ICLR 2025 · similarity 0.89)
- One-Step Diffusion Distillation through Score Implicit Matching (NeurIPS 2024 · similarity 0.89)
- Constrained Diffusion Models via Dual Training (NeurIPS 2024 · similarity 0.89)
- Dimension-free Score Matching and Time Bootstrapping for Diffusion Models (NeurIPS 2025 · similarity 0.88)
- No Training, No Problem: Rethinking Classifier-Free Guidance for Diffusion Models (ICLR 2025 · similarity 0.88)
- Training Diffusion-based Generative Models with Limited Data (ICML 2025 · similarity 0.88)
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