Generative Diffusion Models for High-Dimensional Time Series

We provide a two-stage approach for high dimensional time series generation: (i) kernel estimation for the conditional first and second moments of the underlying data increments to recover residuals, and (ii) score-based diffusion trained on these residuals. We give finite-time convergence estimates for the reverse SDE in total variation (TV) and Wasserstein-2 ($W_2$), with explicit dependence on the variance preserving noise schedule, a corrected initial mismatch of Gaussian targets, and a Grönwall coupling that separates initialization, score and discretization errors. Experiments on synthetic multivariate processes validate: (a) empirical TV and $W_2$ track the theoretical upper bounds, and (b) Monte Carlo estimates of test functionals achieve the predicted standard errors.