Closing the Loop: Co-Evolving EM for Irregular Time Series Generation in Lifted Representations

Regular time-series generation from irregular time series is typically reduced to one-shot imputation: complete each partial sequence once, freeze the completions, and train a generator on the resulting surrogate dataset. We show that this open-loop strategy is structurally flawed. Point imputers collapse ambiguous missing regions to conditional averages, while stochastic imputers become stale as the generator evolves; the binding constraint is therefore iteration, not imputer design. We introduce a co-evolving Monte Carlo EM framework that closes the imputer-generator loop. Each E-step samples missing values from the posterior of the current generator, and each M-step retrains the generator on these completions, preserving unconditional generator training. Since our diffusion prior operates in a lifted 2D representation while observations live in time-series space, we further introduce Posterior Sampling for Lifted Representations (PSLR), which enforces operator-consistent conditioning, uncertainty preservation, and manifold consistency during the E-step. Across ten datasets and four corruption regimes, our method achieves state-of-the-art performance, improving over the strongest baselines by 59% in discriminative score, 15% in predictive score, 73% in Context-FID, and 71% in feature-correlation error. Ablations show that our approach reduces average discriminative score by 73% over single-step baselines, closing most of the remaining gap to the clean-data oracle. Code is available at https://github.com/azencot-group/PSLR.