Satellite sea surface temperature (SST) observations are frequently obscured by cloud cover, creating large gaps that must be reconstructed for many oceanographic and climate applications. Because multiple high-resolution SST fields may be consistent with the same sparse observations, this reconstruction problem is inherently ambiguous. Nevertheless, most existing approaches remain deterministic, producing a single estimate that is often overly smooth, may contain unrealistic artifacts, and provides limited or unreliable uncertainty estimates. To address these limitations, we introduce DIRECT, a conditional generative framework for dense SST reconstruction that models the full distribution of plausible solutions rather than a single deterministic estimate. DIRECT is based on a rectified flow-matching formulation, conditioned on temporal context and day-of-year seasonality, and presents an observation-guided rectification that anchors the generative trajectory to measured pixels at every integration step. By sampling multiple reconstructions, DIRECT produces an ensemble of physically plausible SST fields, enabling both an accurate mean reconstruction and spatially resolved uncertainty estimates that are calibrated using a lightweight post-hoc variance correction. Experiments on three Level-3 SST datasets (Mediterranean, Adriatic, and Atlantic) show that DIRECT sets a new state-of-the-art, reducing Root Mean Square Error (RMSE, in °C) by 6–14 % compared with the strongest published method, while better preserving mesoscale structure. Further analysis of spatial scale correlations indicates that DIRECT maintains physically consistent textures even when reconstructing large, completely unobserved regions. Performance improvements remain robust across a wide range of cloud-coverage conditions, enabling reliable SST reconstruction from sparse satellite observations over much of the global ocean.