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TFG-Flow: Training-free Guidance in Multimodal Generative Flow
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Proposes TFG-Flow, a training-free guidance method for multimodal (discrete + continuous) flow matching models that guides molecule generation toward target properties using off-the-shelf predictors.
Problem
Training-free guidance has been developed for continuous diffusion, but guiding multimodal generative flows over both discrete atom types and continuous 3D coordinates, where discrete guidance suffers from the curse of dimensionality, remains under-explored.
Approach
Constructs a guided multimodal flow that preserves unconditional marginals and aligns with a target predictor, estimates the guided discrete rate matrix by consistent Monte-Carlo importance-weighted sampling (K=O(log(n|A|)) samples) instead of exact enumeration, and guides continuous coordinates via gradient ascent on the predicted endpoint while keeping SO(3) invariance via EGNN and centering pro
Key results
- On QM9 single-property guidance, TFG-Flow achieves the best training-free MAE on all listed properties, e.g., alpha MAE 2.32 vs 3.90 for TFG (best training-free baseline), with an average relative improvement of +20.3% over the best continuous-diffusion training-free baseline.
- Structure guidance raises Tanimoto similarity over unconditional generation by 76.83% on QM9 (0.290) and 22.35% on GEOM-Drug (0.208).
- On CrossDocked2020 pocket-targeted design, TFG-Flow reaches Vina score -7.65 versus -7.01 for unguided Multiflow and -7.32 for TargetDiff, the best among compared methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TFG-Flow instead of TFG for single quantum-property guidance | QM9 molecular generation · QM9, six single quantum-property guidance tasks | MAE: +20.3% average relative improvement over the best training-free guidance method TFG | Helped |
| Use TFG-Flow instead of Cond-Flow for combined quantum-property guidance | QM9 molecular generation · QM9, combined quantum-property guidance | MAE | Helped |
| Use TFG-Flow instead of Cond-Flow for single quantum-property guidance | QM9 molecular generation · QM9, single quantum-property guidance | MAE | No clear effect |
| Apply TFG-Flow structure guidance instead of unconditional generation | Multiflow · QM9 structure guidance | Tanimoto similarity: +76.83% | Helped |
| Apply TFG-Flow structure guidance instead of unconditional generation | Multiflow · GEOM-Drug structure guidance | Tanimoto similarity: +22.35% | Helped |
| Guide Multiflow with TFG-Flow | Multiflow · CrossDocked2020 pocket-targeted drug design | Vina score: $-$7.01$^{\pm1.81}$ -> $\textbf{$-$7.65}^{\pm1.89}$ | Helped |
| Increase continuous guidance iterations from 4 to 8 (ablation) | TFG-Flow · QM9, α guidance | MAE | No clear effect |
| Use approximately 16 Monte Carlo samples for discrete guidance (ablation) | TFG-Flow · QM9, α guidance | MAE: K≈16 | No clear effect |
| Increase guidance strength ρ too strongly (ablation) | TFG-Flow · QM9, α guidance | validity | Hurt |
| Increase temperature τ too strongly (ablation) | TFG-Flow · QM9, α guidance | validity | Hurt |
| Increase guidance strength ρ too strongly (ablation) | TFG-Flow · QM9, α guidance | MAE | No clear effect |
| Increase temperature τ too strongly (ablation) | TFG-Flow · QM9, α guidance | MAE | No clear effect |
Surprising findings
- Training-free guidance still underperforms the training-based EEGSDE by a large margin on quantum property guidance.
- Structure guidance Tanimoto similarities (0.290 and 0.208) are described by the authors as not satisfactory.
Limitations
- Performance gap remains between training-free guidance and training-based methods such as EEGSDE.
- Structure guidance similarity remains low (0.290 on QM9, 0.208 on GEOM-Drug).
- Guidance strengths rho and tau are tuned by grid search and not scheduled over time.
Experimental setup
Datasets: QM9 GEOM-Drug CrossDocked2020
Benchmarks: QM9 quantum property guidance GEOM-Drug structure guidance CrossDocked2020 pocket-targeted drug design
Metrics: MAE Tanimoto similarity Vina score QED SA
Baselines: DPS LGD FreeDoM MPGD UGD TFG Cond-EDM EEGSDE UniGEM Cond-Flow AR Pocket2Mol
Builds on: Multiflow rectified flow TFG EDM EEGSDE
Closest papers by meaning
- Active Flow Expansion for Out-of-Distribution Discovery: from Theory to Molecules (NeurIPS 2026 · similarity 0.90)
- Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning (NeurIPS 2025 · similarity 0.89)
- TFG: Unified Training-Free Guidance for Diffusion Models (NeurIPS 2024 · similarity 0.89)
- Greed is Good: A Unifying Perspective on Guided Generation (NeurIPS 2025 · similarity 0.89)
- Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models (NeurIPS 2025 · similarity 0.89)
- D-Flow: Differentiating through Flows for Controlled Generation (ICML 2024 · similarity 0.88)
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