Imaging Photoplethysmography (iPPG), an optical procedure which recovers a human's blood volume pulse (BVP) waveform using pixel readout from a camera, is an exciting research field with many researchers performing clinical studies of iPPG algorithms. While current algorithms to solve the iPPG task have shown outstanding performance on benchmark datasets, no state-of-the art algorithms, to the best of our knowledge, performs test-time sampling of solution space, precluding an uncertainty analysis that is critical for clinical applications. We address this deficiency though a new paradigm named Regularized Interpolants with Stochasticity for iPPG (RIS-iPPG). Modeling iPPG recovery as an inverse problem, we build probability paths that evolve the camera pixel distribution to the ground-truth signal distribution by predicting the instantaneous flow and score vectors of a time-dependent stochastic process; and at test-time, we sample the posterior distribution of the correct BVP waveform given the camera pixel intensity measurements by solving a stochastic differential equation. Given that physiological changes are slowly varying, we show that iPPG recovery can be improved through regularization that maximizes the correlation between the residual flow vector predictions of two adjacent time windows. Experimental results on three datasets show that RIS-iPPG provides superior reconstruction quality and uncertainty estimates of the reconstruction, a critical tool for the widespread adoption of iPPG algorithms in clinical and consumer settings.