VDSA: Calibrated Financial Forecasting via Few-Step Parameter-Space Diffusion in Selective State Space Models

Financial and macroeconomic time series exhibit non-stationary dynamics, regime switches, and heavy-tailed shocks, making calibrated uncertainty as important as point accuracy. Existing probabilistic state space sequence models often represent dynamics uncertainty with unimodal Gaussian reparameterizations, which can be mis-specified when the posterior over latent dynamics is multi-modal or heavy-tailed. We therefore developed the Variational Diffusion Spectral Adapter (VDSA), a parameter-space generative reparameterization that models the posterior over state transition eigenvalues as a context- conditioned diffusion process. VDSA is integrated with a selective state space model (SSM) backbone: the backbone encodes context while the diffusion module generates context-conditioned spectral samples, inducing a predictive distribution through SSM rollouts. To make diffusion inference deployable, we introduce few-step deterministic sampling and teacher-student distillation that compress sampling to 2–8 denoising steps while preserving calibration. We evaluate VDSA on Exchange Rate, Monash Archive datasets, and a synthetic regime-switching benchmark using point error, proper scoring rules, interval calibration, and tail-risk diagnostics. On Exchange Rate at horizon 30, VDSA reduced CRPS from 0.0364 for a Gaussian spectral posterior to 0.0351 and improved 80% interval coverage from 0.78 to 0.79, while maintaining MAE comparable to deterministic SSM baselines. VaR exceedance rates also moved closer to the nominal 5% level (0.052 vs. 0.061). Few-step inference achieved substantially higher throughput than full diffusion (relative throughput 0.35 at 4 steps vs. 0.12 at 50 steps). The empirical design employs a "baseline evidence mapping table" that maps each comparison method to the corresponding results table, paired statistical tests, VaR backtests, and details regarding reproducibility. These results indicate that parameter space diffusion is a practical mechanism for achieving calibrated forecasts under institutional uncertainty. They also demonstrate that the primary advantage of the method proposed in this paper lies in its probabilistic calibration capability, rather than in an absolute lead in point forecast error.