As retrieval-augmented generation (RAG) systems scale, ensuring faithful grounding in external evidence remains challenging. Large language models may still rely on parametric knowledge when it conflicts with retrieved information. We propose Grounded Decoding, a training-free decoding framework that improves factual consistency in RAG without modifying model parameters. At each generation step, our method constructs two matched-prompt distributions: a full RAG distribution conditioned on the query, retrieved documents, and generated prefix, and a retrieval-only distribution conditioned solely on the retrieved evidence and the same prefix. We derive the final next-token distribution as the unique solution to a KL-barycenter objective over the probability simplex, resulting in a normalized geometric fusion of the two distributions. The formulation recovers standard RAG when the grounding weight is zero and progressively shifts probability mass toward retrieved evidence as grounding strength increases. We further introduce a conflict-aware adaptive weighting scheme that adjusts grounding strength based on distributional disagreement and retriever confidence. Experiments on ALCE, Natural Questions, and FActScore show consistent improvements in factual accuracy and citation quality over standard RAG and competitive decoding-time baselines while maintaining fluency. These results suggest that probability-level fusion offers an effective and efficient alternative to logit-level intervention for faithful RAG decoding.

Process reward models (PRMs) are widely used in language-model training with dense, step-level supervision. They assume that PRM scores remain stable proxies for step correctness under label-preserving transformations that alter reasoning structure while preserving final answers. However, this assumption remains insufficiently validated. Such transformations may alter the relationship between PRM scores and correctness, producing different failure modes across models. To address this gap, we introduce EST-PRM, a stress-testing framework for dense process rewards. It evaluates three transformations: (1) step inflation, (2) dependency-aware step reordering, and (3) confidence markers. We further define a vulnerability decomposition that separates reward inflation from loss of correctness sensitivity. We evaluate five PRM-style models on 4,687 reasoning chains from MATH-500, GSM8K, and PRMBench. Results reveal substantial differences in vulnerability patterns across models. Math-Shepherd exhibits the strongest sensitivity to position-based perturbations, with a Pearson correlation drop of 0.139 ± 0.031 and a 29.7 ± 4.2% score inflation rate, while Qwen2.5-Math-PRM is most affected by step inflation, reaching a 47.6 ± 4.3% inflation rate. Confidence-based perturbations further distort reward calibration, revealing inconsistencies in correctness estimation. Finally, we evaluate three mitigation strategies and identify trade-offs between robustness coverage and false-positive rates.