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We study the issue of finite-time synchronization pertaining to a class of Clifford-valued neural networks with discrete and infinite distributed delays and impulse phenomena. Since multiplication of Clifford numbers is of non-commutativity, we decompose the original <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-dimensional Clifford-valued drive and response systems into the equivalent <inline-formula> <tex-math notation="LaTeX">$2^{m}$ </tex-math></inline-formula>-dimensional real-valued counterparts. We then derive the finite-time synchronization criteria concerning the decomposed real-valued drive and response models through new Lyapunov-Krasovskii functional and suitable controller as well as new computational techniques. We also demonstrate the usefulness of the results through a simulation example.