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D-DOIT: Training-free Adaptation of Discrete Diffusion via Doob's h-Transform

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Diffusion theory and design space · 0 citations (OpenAlex)

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Proposes D-DOIT, a training-free sampler that applies a discrete Doob h-transform to frozen masked discrete diffusion models, using prediction-head completions and reward values to guide reverse transitions toward reward-tilted targets for DNA enhancer and protein inverse-folding design.

Problem

Adapting frozen masked discrete diffusion models (DNA and protein sequence design) to black-box, non-differentiable sequence-level rewards without retraining the backbone and without expensive rollouts.

Approach

Applies Doob's h-transform at the kernel level for categorical masked diffusion: reverse transition probabilities are multiplicatively reweighted by a downstream value estimated by one prediction-head clean completion scored by the reward, with finite-candidate resampling and optional late best-of-K branching.

Key results

• On HepG2 enhancer design, D-DOIT-Q reaches Pred-Activity above DRAKES (training-based) on activity, 3-mer Corr 0.894 and JASPAR Corr 0.923, while ATAC-Acc 91.7% is slightly below DRAKES 92.5%.
• On protein inverse folding, D-DOIT achieves 68.1% joint success versus 63.6% (SMC) and 62.9% (TDS), with the highest Pred-ddG of 0.870.
• On Ctrl-DNA, D-DOIT-Q raises specificity Delta R to 0.119 with a trade-off in motif correlation (0.498 vs 0.937 for pre-trained).

Surprising findings

• Uncorrected tempered proposals and sharpening deviate from the exact target, and the authors note the practical sampler does not inherit the exact-target guarantee.
• On Ctrl-DNA, endpoint search (Frozen Best-of-708) captures much of the specificity gain, so the margin over matched-time baselines is smaller than on HepG2.

Limitations

• Practical approximations (tempering, sharpening, best-of-K selection, single-step prediction-head h-estimator) introduce bias and lose the exact-target guarantee.
• Evaluation relies on predictive oracles without experimental biological validation.
• Highest-quality setting (D-DOIT-Q) incurs substantial inference cost relative to training-free baselines.

Experimental setup

Datasets: DRAKES HepG2 enhancer benchmark Ctrl-DNA cell-type-specific enhancer benchmark DRAKES protein inverse-folding benchmark

Benchmarks: DRAKES HepG2 enhancer design Ctrl-DNA cell-type-specific enhancer design DRAKES protein inverse folding

Metrics: Pred-Activity ATAC-Acc 3-mer Corr JASPAR Corr Delta R specificity Motif Corr Pred-ddG scRMSD joint success rate

Baselines: CG SMC TDS SVDD-PM Frozen Best-of-708 DRAKES CFG DRAKES w/o KL regLM Ctrl-DNA

Builds on: DRAKES soft value-based decoding twisted diffusion sampler masked discrete diffusion

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