Retrieval-Warmed Energy-Based Reasoning: A Five-Arm Ablation Methodology for Diffusion-as-Inference on Structured Reasoning Tasks

Warm-started diffusion samplers accelerate iterative inference, but it is rarely clear which part of the pipeline carries the gain. We study retrieval-warmed energy-based reasoning (RW-EBR) -- an IRED energy-based diffusion model citedu2024ired augmented with a Modern Hopfield trajectory memory -- and contribute a five-arm ablation methodology (oracle, best-constant, per-query-random, shuffled, aligned) that separates three confounded effects: class-prior bias shift, stochastic warm-starting, and graph-aligned value reuse. The diagnostic decomposition is adapted from LLM-RAG evaluation citeru2024ragchecker. On connectivity-2 (ErdHos--R'enyi all-pairs reachability), the aligned-vs-shuffled-oracle swing reaches +35,pp balanced accuracy on a fixed 1,000-graph validation-set diagnostic, with value distribution and retrieval mechanics fixed, only per-graph alignment destroyed, while per-query random initialisation falls below cold -- per-graph alignment, not bias shift or stochasticity, dominates. Yet the deployable cold-prediction pipeline misses the acceptance gate at stored-value quality. The same diagnostic logic, stopped at the key-quality screen, applied to Sudoku with a task-specific key encoder produces a clean negative at a different component -- key quality, under the current setup. The decomposition names the first blocking component on each task. The setting -- graph reachability refined by an iterative diffusion sampler, with explainability of failure modes as the lens -- places the work within structured and spatio-temporal reasoning.