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Preference-Guided Diffusion for Multi-Objective Offline Optimization
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Proposes PGD-MOO, a diffusion model with classifier guidance from a Bradley-Terry-style preference model predicting Pareto dominance between designs, with crowding-distance-based diversity labels, for offline multi-objective optimization.
Problem
Offline multi-objective optimization: find Pareto-optimal and well-spread designs using only a fixed dataset of designs and objective values, without sequential evaluation.
Approach
Replaces per-objective surrogate classifiers with a time-conditioned preference classifier that predicts whether one design Pareto-dominates another; training pairs with equal dominance rank are labeled by crowding distance so guidance favors diverse front members, and this guidance steers an unconditional DDPM toward the Pareto set.
Key results
- PGD-MOO achieves average hypervolume ranking 4.42 on synthetic tasks and 1.86 on MO-NAS, the best among methods.
- PGD-MOO has the best average Delta-spread ranking on synthetic (2.83) and RE (4.28) tasks, ahead of all baselines including ParetoFlow (10.0 and 9.0).
- On RE tasks PGD-MOO ranks 7.67 in hypervolume, behind MultipleModels (3.67), so it is not uniformly best in convergence.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use preference-guided diffusion instead of the evaluated methods | offline MOO · Synthetic tasks | average hypervolume rank: 5.08 -> 4.42 | Helped |
| use preference-guided diffusion instead of the evaluated methods | offline MOO · RE tasks | average hypervolume rank: 3.67 -> 7.67 | Hurt |
| use preference-guided diffusion instead of the evaluated methods | offline MOO · MO-NAS tasks | average hypervolume rank: 2.72 -> 1.86 | Helped |
| use preference-guided diffusion rather than ParetoFlow | offline MOO · Synthetic tasks | average hypervolume rank: 7.58 -> 4.42 | Helped |
| use preference-guided diffusion rather than ParetoFlow | offline MOO · Synthetic tasks | average Δ-spread rank: 10.0 -> 2.83 | Helped |
| increase guidance weight from 0 to 50 (ablation) | PGD-MOO · ZDT2 | hypervolume: 5.20±0.03 -> 5.62±0.04 | Helped |
| increase guidance weight from 0 to 50 (ablation) | PGD-MOO · ZDT6 | Δ-spread: 0.77±0.05 -> 0.91±0.04 | Hurt |
| add a diversity criterion using Crowding instead of no diversity (ablation) | PGD-MOO preference-pair selection · DTLZ2 | Δ-spread: 0.55±0.00 -> 0.56±0.02 | Helped |
| add a diversity criterion using Crowding instead of no diversity (ablation) | PGD-MOO preference-pair selection · RE35 | Δ-spread: 0.90±0.02 -> 1.00±0.12 | Helped |
| replace Crowding with Hypervolume for preference-pair selection (ablation) | PGD-MOO · Synthetic and RE tasks | Δ-spread | Mixed |
| train the preference model using only the top 30% of points (ablation) | PGD-MOO · Synthetic tasks | average hypervolume rank: 4.42 -> 5.08 | Hurt |
Surprising findings
- Guidance weight w=0 (no preference guidance) gives only modestly lower hypervolume on several DTLZ tasks, and on some tasks it is near the guided versions.
Limitations
- Relies only on dominance information, not objective values, so it offers no fine-grained control over trade-offs.
- Slightly worse hypervolume than baselines on problems with more objectives, per the authors.
- Ablation on diversity criteria shows mixed gains; differences across criteria are often within noise.
Experimental setup
Datasets: Synthetic MOO benchmark (DTLZ, ZDT) RE engineering suite MO-NAS (C-10/MOP1-9, IN-1K/MOP1-9)
Benchmarks: DTLZ ZDT RE MO-NAS
Metrics: hypervolume delta-spread average ranking
Baselines: ParetoFlow MultiHead MultiHead-PcGrad MultiHead-GradNorm MultipleModels MultipleModels-COM MultipleModels-IOM MultipleModels-ICT MultipleModels-RoMA MultipleModels-TriMentoring
Builds on: classifier guidance DDPM NSGA-II ParetoFlow
Closest papers by meaning
- ParetoFlow: Guided Flows in Multi-Objective Optimization (ICLR 2025 · similarity 0.91)
- FERERO: A Flexible Framework for Preference-Guided Multi-Objective Learning (NeurIPS 2024 · similarity 0.89)
- Interactive Hyperparameter Optimization in Multi-Objective Problems via Preference Learning (AAAI 2024 · similarity 0.88)
- MODULI: Unlocking Preference Generalization via Diffusion Models for Offline Multi-Objective Reinforcement Learning (ICML 2025 · similarity 0.88)
- User Preference Meets Pareto-Optimality in Multi-Objective Bayesian Optimization (AAAI 2025 · similarity 0.88)
- Amortized Active Generation of Pareto Sets (NeurIPS 2025 · similarity 0.87)
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