# VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusion

arXiv: https://arxiv.org/abs/2608.26585 · HTML: https://mlsanity.com/paper/2608.26585/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 35 of its 52 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 35)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design](https://mlsanity.com/paper/2410.13643/) (2024)
- [Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator](https://mlsanity.com/paper/2010.04838/) (2020)
- [Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction](https://mlsanity.com/paper/2410.08134/) (2024)
- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [Split Gibbs Discrete Diffusion Posterior Sampling](https://mlsanity.com/paper/2503.01161/) (2025)
- [Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Design](https://mlsanity.com/paper/2505.22524/) (2025)
- [Discrete Diffusion Trajectory Alignment via Stepwise Decomposition](https://mlsanity.com/paper/2507.04832/) (2025)
- [Discrete Feynman-Kac Correctors](https://mlsanity.com/paper/2601.10403/) (2026)
- [What Exactly Does Guidance Do in Masked Discrete Diffusion Models](https://mlsanity.com/paper/2506.10971/) (2025)
- [Effective Test-Time Scaling of Discrete Diffusion through Iterative Refinement](https://mlsanity.com/paper/2511.05562/) (2025)
- [Inference-Time Scaling of Diffusion Language Models via Trajectory Refinement](https://mlsanity.com/paper/2507.08390/) (2025)
- [Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Design](https://mlsanity.com/paper/2602.09424/) (2026)

## Built on by (most cited first, 1 of 1)

- [Risk-Calibrated Proposal Transport for Finite-Particle Diffusion Steering](https://mlsanity.com/paper/2610.04171/) (2026)

## Abstract (arXiv)

Masked discrete diffusion models perform strongly on text, code, and biological sequences, but their training objective rewards only naturalness, and retraining the generator for every new reward is expensive. Inference-time steering of a frozen model either guides the sampler by the reward gradient or searches over several trajectories, and recent samplers combine the two. Such combinations are assembled as pipelines that leave three choices at their defaults: a guidance estimate resting on one Gumbel draw per sample, a reward tilting placed without reference to the distribution the combination then targets, and a selection temperature held fixed although the spread of per-step rewards drifts. We identify that distribution and settle the three choices against it. We therefore propose Variance-reduced Guidance and Adaptive Selection (VGAS), a simple yet effective inference-time framework that reduces the variance of the guidance estimate for both reward types, applies the reward tilting in the clean-token logits, where the pretrained schedule is preserved, and sets the selection temperature per step. Across regulatory DNA, protein and small-molecule benchmarks, VGAS attains the best training-free reward and matches or surpasses a reward-fine-tuned generator.