EM-style Framework for Task-Driven Differentiable Synthesizer Optimization: Rationale, Design, and Backpropagation through Reaction–Diffusion System

Author contact: yan.yang.research [at] proton.me This technical report presents a diagnostic study on differentiable synthesizer optimization. It consists of two closely related but distinct parts. Part I examines the rationale for using downstream-task feedback to optimize synthetic data genera- tors. We revisit the motivation originating from Klein et al. [17, 19], analyze its empirical limitations, and discuss supporting evidence from Meta-Sim and Task2Sim. We then introduce an EM-style framework design that alternates between trainer and synthesizer optimization. Part II investigates backpropagation through reaction–diffusion systems, a concrete and challenging instantiation of the differentiable synthesizer that was explored during the development of the EM-style framework. We provide theoretical details of several approaches (truncated BPTT with intermediate supervision, implicit differentiation, adjoint method, and Krylov solver), present an empirical diagnosis of the loss landscape on a Gray-Scott system, and outline renewed solution directions. Code and experimental materials are available at https://github.com/Yan-Yang-bot/bp2renderer. Note added on April 12, 2026: A comprehensive survey of traditional inverse problem methods was not conducted at the time of the original deposit. These classical techniques will be reviewed and potentially integrated if the framework is extended to real neuroscience data applications (as I aim to do in future work).