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Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models
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Proposes TreeG, a tree-search path-steering framework for training-free guidance of diffusion and flow models that handles non-differentiable objectives and discrete data, instantiated as TreeG-SC, TreeG-SD and TreeG-G, and reports an inference-time scaling law.
Problem
Training-free guidance of diffusion and flow models usually relies on gradients and differentiable objectives, which fails for non-differentiable objectives and discrete data distributions.
Approach
Unifies guidance as propose-evaluate-select over an active set of paths: each path branches into K candidates (sampled from the current state or from a predicted clean destination), candidates are scored by a value function built from the off-the-shelf objective, and the top A are kept, enabling zeroth-order guidance with tree search and parallel exploration.
Key results
- TreeG-SD reduces music pitch-histogram loss to 0.0002 vs 0.0010 for DPS, and reports an average 29.01% loss reduction.
- TreeG-SC (K=4) achieves 0.79 QED validity vs 0.61 for no guidance and 0.62 for DG, with an average 16.6% improvement across molecule targets.
- TreeG-G reaches target class probability 0.560, 0.951 and 0.894 for three DNA classes at strength 200, with an average 18.43% improvement over DG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TreeG-SD instead of the strongest reported baseline | Piano diffusion model · Pitch Histogram | Loss: 0.0010 ± 0.0020 -> 0.0002 ± 0.0003 | Helped |
| Use TreeG-SD instead of SCG | Piano diffusion model · Note Density | Loss: 0.134 ± 0.533 -> 0.142 ± 0.423 | Hurt |
| Use TreeG-SD instead of SCG | Piano diffusion model · Chord Progression | Loss: 0.347 ± 0.212 -> 0.301 ± 0.191 | Helped |
| Use TreeG-SC (K=4) instead of SVDD | Discrete flow model · QED | VAL: 0.71±0.17 -> 0.79 ± 0.12 | Helped |
| Use TreeG-SC (K=4) instead of SVDD | Discrete flow model · SA | VAL: 0.81±0.09 -> 0.90±0.07 | Helped |
| Use TreeG-SC (K=4) instead of SVDD | Discrete flow model · DRD2 | VAL: 0.64±0.42 -> 0.77±0.33 | Helped |
| Use TreeG-SC (K=4) instead of DG | Discrete flow model · N_r*=1 | MAE: 0.11±0.33 -> 0.01±0.07 | Helped |
| Use TreeG-G (γ=200) instead of DG (γ=100) | DNA discrete flow model · Class 1 | Prob: 0.372 ± 0.237 -> 0.560 ± 0.258 | Helped |
| Use TreeG-G (γ=200) instead of DG (γ=20) | DNA discrete flow model · Class 2 | Prob: 0.627 ± 0.340 -> 0.951 ± 0.110 | Helped |
| Use TreeG-G (γ=200) instead of DG (γ=20) | DNA discrete flow model · Class 3 | Prob: 0.693 ± 0.264 -> 0.894 ± 0.136 | Helped |
| Use TreeG-SC instead of TreeG-G | Discrete flow model · Molecule generation (N_r=2) | MAE: 0.09±0.54 -> 0.02±0.14 | Helped |
| Use TreeG-SC instead of TreeG-SD | Discrete flow model · Molecule generation (N_r=2) | MAE: 0.10±0.33 -> 0.02±0.14 | Helped |
Surprising findings
- TreeG-SD requires far more samples for discrete flow models and underperforms TreeG-SC there, while it is preferred for continuous music generation.
- Selection by ranking was empirically found superior to resampling, despite theory being given for resampling.
Limitations
- Can be time-consuming when the objective is non-differentiable, expensive to evaluate, and lacks a surrogate predictor.
- Theoretical guarantees rely on idealized assumptions such as a perfect pre-trained model and Gaussian data with linear objective for the continuous case.
- TreeG-SD is inefficient for discrete flow models, requiring many more samples.
Experimental setup
Datasets: piano MIDI datasets SMILES molecule data enhancer DNA sequences with 81 cell types
Benchmarks: symbolic music guidance targets (pitch histogram, note density, chord progression) small molecule QED/SA/DRD2/ring count enhancer DNA cell-type guidance
Metrics: loss overlapping area validity Tanimoto similarity MAE target class probability Frechet Biological Distance diversity
Baselines: DPS TDS SCG SVDD DG TFG-Flow
Builds on: DPS SVDD TDS TFG-Flow Discrete Flow Matching
Closest papers by meaning
- TFG-Flow: Training-free Guidance in Multimodal Generative Flow (ICLR 2025 · similarity 0.89)
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