Denoising Subordinated Probabilistic Models: Diffusion with a Tempered-Stable Volatility Clock, and What the Noise Mechanism Actually Controls

Battle Count: 51

The paper is primarily a methodological/theoretical contribution to generative modeling of financial time series. Its direct relevance to quantitative trading is moderate: it provides a principled framework for generating realistic return paths with volatility clustering and heavy tails, which is foundational for backtesting, scenario generation, and risk simulation. The nuisance-invariance theorem has practical implications for how heavy-tailed noise choices in diffusion models should be interpreted. However, the paper does not directly address trading strategies, execution, or portfolio construction. The v2 coupling (control via interventions) could enable scenario-based stress testing relevant to risk management. The work is more foundational than immediately actionable for trading.

The core DSPM (v1) is relatively straightforward: it is 'verbatim DDPM with D_A^{1/2} scalings' plus an AR(1) tempered-stable chain simulation. The sampler uses Kanter's representation with exponential-tilting rejection. However, the full v2 coupled model requires: (1) variational encoder with coarse bottleneck, (2) log-normal OU prior with learned parameters, (3) the SV-ELBO term (log-determinant of noise covariance) which simplified diffusion losses omit, (4) careful handling of KL weight to avoid collapse or leakage. The theoretical machinery (tempered stable subordinators, BNS process, nuisance invariance proof) requires significant mathematical background. Training is cheap (minutes on laptop) but understanding the design choices and failure modes requires careful reading.

All derivations and every number are reproduced by accompanying scripts (01_sampler_check.py through 07_blind.py, plus 08-09 for v2). Fixed seeds throughout. Runs on a single Apple-Silicon laptop in minutes. Core code files (dspm_core.py, dspm_net.py) are referenced. Three training seeds for headline comparisons. The paper explicitly states 'All derivations and every number in this paper are reproduced by the accompanying scripts.'