Process Reward Modeling with Reliability- and Conservatism-Aware Bayesian Belief

Process Reward Models (PRMs) play a central role in test-time scaling for large language model (LLM) reasoning. However, PRMs may provide inaccurate process rewards for test-time scaling, which we identify as arising from two sources of uncertainty: (1) $\mathit{\text{PRM}}\mathit{\text{uncertainty}}$ that arises from insufficient supervision data and imperfect PRM training; and (2) $\mathit{\text{policy}}\mathit{\text{uncertainty}}$ that results from the mismatch between the policy to collect supervision data and the policy for test-time scaling, leading to systematic reward overestimation. Previous studies fail to jointly consider both uncertainties. To bridge this gap, we propose BayesianPRM, which treats the process reward as a random variable within a reward hypothesis space and maintains a Bayesian belief over it. Since exact Bayesian inference over the continuous hypothesis space is generally intractable, we discretize the reward hypothesis space with a reward ensemble and introduce two complementary belief updates, each targeting one source of uncertainty: (1) to address PRM uncertainty, we introduce $\mathit{\text{reliability-aware}}\mathit{\text{belief}}\mathit{\text{updating}}$ that measures how well each ensemble member explains the supervision data and updates the belief with an amortized belief network optimized by the evidence lower bound (ELBO); and (2) to tackle policy uncertainty, we propose $\mathit{\text{conservatism-aware}}\mathit{\text{belief}}\mathit{\text{calibration}}$ which further reweights the belief toward lower rewards to suppress overestimation. These two updates yield a reliability- and conservatism-aware Bayesian belief, whose expectation determines the process reward. Experiments on multimodal reasoning benchmarks indicate that BayesianPRM consistently yields more accurate process reward estimates while enhancing test-time scaling performance.