Patient-specific models based on coronary arteries segmented from CT-scans have been widely used to simulate blood flow and to identify flow-limiting lesions through fractional flow reserve predictions [1]. However, an important remaining challenge is the integration of multiple spatial scales of the cardiovascular system (from large arteries to the microcirculation) in order to accurately quantify myocardial blood flow. Previous work [2] proposed a multiscale framework to predict left ventricular myocardial perfusion by integrating the generation of synthetic arterial trees extending from segmented coronary arteries and hemodynamic models. This model couples a 1D Navier–Stokes model in both segmented and synthetic arteries with a single-compartment Darcy model for myocardial perfusion. Although promising results were obtained, uncertainties in microvascular geometry and physiological parameters limit the accuracy of perfusion maps for certain patients. Machine learning (ML) models trained directly on medical imaging could help infer missing information, but their effectiveness is often constrained by the limited availability of patient data. Recently, hybrid ML–CFD approaches [3] have emerged as a way to add physical prior-knowledge to the training of a ML model through PDE-based losses or differentiable solvers to improve generalization and reduce data requirements. In this study, we developed a fully differentiable solver for myocardial perfusion simulation. The framework integrates a differentiable 1D Navier–Stokes solver for coronary arteries with a finite-volume–informed graph neural network [4] for the Darcy perfusion model. Using PyTorch automatic differentiation, we simulated myocardial blood flow in patients with obstructive and non-obstructive coronary artery disease using a gradient-based optimization method. The results show low myocardial blood flow errors compared to baseline simulations (mean relative error < 5% across tested patients), highlighting robust gradient propagation and the potential of this approach for end-to-end learning and inverse problems, such as fitting PET-derived perfusion measurements for non-invasive assessment of coronary microvascular dysfunction.