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Diffusion models derived from diffusion magnetic resonance imaging (dMRI) can non-invasively probe tissue microstructural features. Accurate estimation of diffusion model parameters is important for understanding the brain’s white matter, but commonly used nonlinear parameter fitting methods are less accurate and extremely slow. We propose an effective deep learning framework (Deep-PICASO) for estimation of multi-fiber parameters for an advanced diffusion model, precise inference and characterization of structural organization (PICASO). Deep-PICASO leverages a novel image representation of dMRI signal and can be trained using synthetic dMRI data. This is quite advantageous as accurate parameter estimates from real data are unavailable. The framework is tested on the synthetic and in-vivo real datasets. Our framework outperforms comparable nonlinear methods by a large margin on parameter estimation tasks, and runs significantly faster than existing methods.