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Unlocking Guidance for Discrete State-Space Diffusion and Flow Models
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Introduces Discrete Guidance, a principled way to apply predictor and predictor-free guidance to CTMC-based discrete diffusion and flow models, with a Taylor-approximated variant (TAG) for efficiency.
Problem
Guidance (classifier and classifier-free) is well developed for continuous diffusion and flow models but not readily applicable to generative models on discrete state-spaces, where score functions are undefined and Bayes-rule normalizing constants are intractable.
Approach
In continuous time, only one dimension of a discrete state changes at a time, so the normalizing constant reduces to D×(S−1)+1 terms; this makes guidance exact via likelihood-ratio modulation of CTMC rates, and a first-order Taylor approximation of the predictor gives a cheap variant (TAG).
Key results
- On small-molecule property guidance (γ=2), Discrete Guidance (exact and TAG) achieved statistically significantly lower MAE to target number of rings and LogP than DiGress.
- On enhancer DNA design, DG-Exact, DG-TAG and DiGress performed comparably, while Dirichlet FM classifier guidance performed worse.
- On stability-guided inverse folding across eight proteins, FMIF-DG-Exact matched or outperformed all other methods on seven of eight proteins.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Discrete Guidance instead of DiGress | Small-molecule generation · QMugs-derived molecules, conditioned on ring count or LogP | property MAE | Helped |
| Replace exact guidance with Taylor-approximated guidance (TAG) (ablation) | Discrete Guidance for small-molecule generation · QMugs-derived molecules, conditioned on ring count or LogP | property MAE | Mixed |
| Use DG-Exact or DG-TAG instead of DirFM-CG | Enhancer DNA generation · Eight cell-type classes | Class-Conditional FBD | Helped |
| Use DG-Exact or DG-TAG instead of DirFM-CG | Enhancer DNA generation · Eight cell-type classes | Class Probability | Helped |
| Replace exact guidance with Taylor-approximated guidance (TAG) (ablation) | Discrete Guidance for enhancer DNA generation · Eight cell-type classes | Class-Conditional FBD | No clear effect |
| Use predictor-free guidance instead of predictor guidance (ablation) | Discrete Guidance for enhancer DNA generation · Enhancer DNA generation | conditional generation performance | No clear effect |
| Add exact or Taylor-approximated stability guidance to FMIF | FMIF inverse-folding model · Eight randomly chosen proteins | success rate | Helped |
| Replace exact guidance with Taylor-approximated guidance (TAG) (ablation) | FMIF inverse-folding model · Eight randomly chosen proteins | success rate | Mixed |
| Use FMIF instead of ProteinMPNN | Inverse folding · Eight randomly chosen proteins | success rate | Helped |
Surprising findings
- Taylor-approximated guidance (TAG) matched or beat exact guidance on some proteins (e.g., 6ACV), attributed to miscalibrated time-dependent predictors.
- Flow-matching inverse folding (FMIF) consistently matched or outperformed ProteinMPNN in the non-guided setting.
Limitations
- TAG lacks the theoretical guarantees of exact guidance.
- Guidance requires training time-dependent predictors on noised samples, and predictor miscalibration can mislead guidance.
- Evaluated on a limited set of tasks; no language model experiments.
Experimental setup
Datasets: QMugs enhancer DNA sequence dataset (104k sequences, 81 cell types) mini-protein stability (ΔΔG) dataset CIFAR-10
Benchmarks: QMugs-derived small-molecule property control (MAE) enhancer DNA class-conditional FBD and class probability stability-guided inverse folding success rate
Metrics: mean absolute error Fréchet Biological Distance class probability success rate (RMSD ≤ 2Å and ΔΔG ≥ 0) validity
Baselines: DiGress Dirichlet FM classifier-free guidance Dirichlet FM classifier guidance ProteinMPNN
Builds on: discrete flow models continuous-time discrete diffusion DiGress predictor-free guidance Dirichlet flow matching
Closest papers by meaning
- Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design (ICML 2024 · similarity 0.91)
- Simple Guidance Mechanisms for Discrete Diffusion Models (ICLR 2025 · similarity 0.91)
- Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-based Decoding (NeurIPS 2025 · similarity 0.89)
- Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspective (ICLR 2025 · similarity 0.89)
- Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design (ICLR 2025 · similarity 0.88)
- Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction (ICLR 2025 · similarity 0.88)
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