MARS‐Diff: Guarded Residual Diffusion for Leakage‐Disciplined Probabilistic Portfolio‐Loss Forecasting

ABSTRACT This paper develops Masked Asset–Regime Scenario Diffusion (MARS‐Diff), a leakage‐disciplined framework for probabilistic forecasting of multiday portfolio losses. The framework combines a regularized heterogeneous autoregressive model with exogenous predictors (HAR‐X) as its anchor, a train‐only masked representation of a high‐dimensional asset panel, train‐only market‐stress conditioning, and conditional residual diffusion. Rather than replacing the anchor, the diffusion correction is admitted only when it weakly improves outer‐validation continuous ranked probability score (CRPS); otherwise, the final forecast reuses the anchor scenario distribution exactly. The empirical application begins with a prespecified universe of 50 exchange‐traded funds and large‐capitalization equities over 2010–2025, of which 49 satisfy the initial‐period availability criterion. At the 5‐day horizon, generalized autoregressive conditional heteroskedasticity (GARCH) benchmarks—specifically exponential GARCH (EGARCH)‐ and Glosten–Jagannathan–Runkle GARCH (GJR‐GARCH)‐—attain lower CRPS than guarded MARS‐Diff and remain significantly better after multiplicity adjustment. The always‐active residual diffusion is statistically indistinguishable from the retained anchor, whereas direct conditional diffusion performs significantly worse. At the 10‐day horizon, guarded MARS‐Diff is statistically indistinguishable in CRPS from the lowest‐CRPS asymmetric GARCH benchmarks in the comparison set, whereas always‐active residual diffusion and direct conditional diffusion produce significantly higher CRPS. Tail‐score evidence is model‐ and horizon‐dependent, and rolling guard diagnostics characterize the admission rule as conservative but imperfect. Controlled experiments further indicate that fitted residual diffusion can improve CRPS in a state‐dependent positive‐control setting, while producing higher losses in anchor‐friendly and financial‐stress environments. The results are therefore consistent with interpreting MARS‐Diff primarily as an anchored validation‐based admission architecture rather than as evidence of uniform diffusion superiority in financial loss forecasting.