Diffusion Magnetic Resonance Imaging (dMRI) sensitises the MRI signal to spin motion. This includes Brownian diffusion, but also flow across intricate networks of capillaries. This effect, the intra-voxel incoherent motion (IVIM), enables microvasculature characterisation with dMRI, through metrics such as the vascular signal fractionfVor Apparent Diffusion Coefficient (ADC)D*. The IVIM metrics, while sensitive to perfusion, are in general protocol-dependent, and their interpretation can change depending on the flow regime spins experience during the dMRI measurements (e.g., diffusive vs ballistic), which is in general not known — facts that hamper their clinical utility. Innovative vascular dMRI models are needed to enable thein vivocalculation of biologically meaningful markers of capillary flow. These could have relevant applications in cancer, for instance assessing responses to anti-angiogenic therapies targeting tumor vessels. This paper tackles this need by introducingSpinFlowSim, an open-source simulator of dMRI signals arising from blood flow within pipe networks. SpinFlowSim, tailored for the laminar flow patterns in capillaries, enables the synthesis of highly-realistic microvascular dMRI signals, given networks reconstructed from histology. We showcase the simulator by generating synthetic signals for 15 networks, reconstructed from liver biopsies, and containing cancerous and non-cancerous tissue. Signals exhibit com-plex, non-mono-exponential behaviours, pointing towards the co-existence of different flow regimes within the same network, and diffusion time dependence. We also demonstrate the potential utility of SpinFlowSim by devising a strategy for microvascular property mapping informed by the synthetic signals, focussing on the quantification of blood velocity distribution moments, and of anapparent network branchingindex. These were estimatedin silicoandin vivo, in healthy volunteers and in 13 cancer patients, scanned at 1.5T. In conclusion, realistic flow simulations, as those enabled by SpinFlowSim, may play a key role in the development of the next-generation of dMRI methods for microvascular mapping, with immediate applications in oncology.