# Why Deterministic PRM Guidance Underperforms in Discrete Diffusion Reasoning

arXiv: https://arxiv.org/abs/2609.35472 · HTML: https://mlsanity.com/paper/2609.35472/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion reasoning and test-time scaling, one of 17 directions in LLM reasoning.
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- LLM reasoning / [Diffusion reasoning and test-time scaling](https://mlsanity.com/lr/diffusion-reasoning-and-test-time-scaling/)
- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 14 of 14)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignment](https://mlsanity.com/paper/2505.11821/) (2025)
- [Dependency-Guided Parallel Decoding in Discrete Diffusion Language Models](https://mlsanity.com/paper/2604.02560/) (2026)
- [Inference-Time Scaling of Diffusion Language Models via Trajectory Refinement](https://mlsanity.com/paper/2507.08390/) (2025)
- [RFG: Test-Time Scaling for Diffusion Large Language Model Reasoning with Reward-Free Guidance](https://mlsanity.com/paper/2509.25604/) (2025)
- [From Solving to Verifying: A Unified Objective for Robust Reasoning in LLMs](https://mlsanity.com/paper/2511.15137/) (2025)

## Abstract (arXiv)

Discrete diffusion language models (dLLMs) expose a denoised solution at every step, which makes process reward model (PRM) guidance look like a way to spend compute at test time. We show that once denoising, PRM scoring, and outcome reward model (ORM) scoring are charged in the same budget of forward passes, its deterministic form loses to a much simpler baseline. Our PRMs score intermediate denoising states and are trained on the correctness of the final answer. On Dream-v0-Instruct-7B with 8 candidates per GSM8K problem, keeping the candidate with the highest PRM score at every scoring step reaches 65.18%, while independent sampling plus an ORM reranker trained for the task reaches 75.13%. The gap grows to 12.69 percentage points (pp) with 32 candidates, and is 9.85 pp on MATH and 12.16 pp on MBPP. We trace it to two separable failures. First, guidance prunes on a weak signal: on GSM8K, PRM ROC-AUC falls from 0.77 to 0.54 as the mask ratio rises, a decay that persists when states are relabeled with fresh rollouts, and pruning lowers the best accuracy reachable from the candidate pool from 81.05% for independent samples to 67.30%. Second, on GSM8K and MATH, the PRM is a poor final judge: a sequential Monte Carlo sampler at the same budget restores that ceiling to 77.89%, yet selecting with the PRM gives 65.48%, on par with deterministic guidance, while a PRM retrained on final states matches the ORM on identical candidates. MBPP separates the two: there the PRM reaches 65.47% when reranking finished programs, on par with the ORM, but 50.88% when it guides denoising. The results point to two targets for dLLM guidance: keep correct partial solutions alive through early denoising, and leave the final choice to a verifier trained on final states. We release the corpus of denoising states with outcome labels and evaluation toolkit for reproducible comparisons at matched compute.