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Spectral Feedback for Test-Time Alignment of Protein Diffusion Models

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Training-free diffusion acceleration · 0 citations (OpenAlex)

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Proposes Spectral Feedback, a black-box test-time alignment loop for discrete diffusion protein inverse folding that selects re-masking edit-sets by sparse Fourier recovery (ProxySPEX) of an edit-set value function.

Problem

Test-time alignment of discrete diffusion models mostly steers the denoising process or selects full samples; choosing which token positions to re-mask and re-sample in a feedback loop is combinatorial because edit effects interact.

Approach

Treat edit-position selection as maximizing an edit-set value function over subsets of positions; empirically this function has a sparse Fourier spectrum (epistasis-like), so a sparse Fourier surrogate (ProxySPEX, or first-order LASSO) can be fit from few samples and optimized via integer programming to pick edit sets, without modifying the diffusion model.

Key results

• On the pretrained model, Spectral Feedback raises average evaluation ddG from -0.49 to 0.33 and success (scRMSD<2) from 91.8% to 94.2%.
• Spectral Feedback on Best-of-10 raises eval ddG from 0.09 to 0.86, with success rising from 92.4% to 96.7%.
• On DRAKES, Spectral Feedback raises eval ddG from 0.99 to 1.38 but lowers success rate from 93.4% to 85.8% due to higher scRMSD.

Surprising findings

• Applied to DRAKES, Spectral Feedback increases average scRMSD (1.17 to 1.53) and reduces the scRMSD<2 success rate despite higher stability reward.
• Sparsity and interaction order vary by protein: some backbones are dominated by first-order terms while others need higher-order interactions.

Limitations

• Value functions are stochastic and require many protein-model calls, making feedback costly.
• Sparse recovery needs a large number of edit-set samples (D=8192) before it works well.
• Structural quality (scRMSD) can degrade when applied to DRAKES, limiting success-rate gains.

Experimental setup

Datasets: Megascale

Benchmarks: Megascale protein backbones (ddG stability)

Metrics: ddG (alignment and evaluation oracle) scRMSD scRMSD<2 success rate ProtGPT2 log-likelihood

Baselines: Best-of-10 DRAKES Gradient-Weighting Token Exclusion Argmax Selection Hill Climbing First-order LASSO

Builds on: DRAKES SPEX ProxySPEX Best-of-N ProteinMPNN

Closest papers by meaning

• Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction (ICLR 2025 · similarity 0.89)
• Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Design (ICML 2025 · similarity 0.88)
• Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design (ICLR 2025 · similarity 0.87)
• Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-based Decoding (NeurIPS 2025 · similarity 0.87)
• Bridge-IF: Learning Inverse Protein Folding with Markov Bridges (NeurIPS 2024 · similarity 0.87)
• D-DOIT: Training-free Adaptation of Discrete Diffusion via Doob's h-Transform (NeurIPS 2026 · similarity 0.87)