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Unlike prior methods that restrict auxiliary components to Gaussian noise, AuxPath-FM allows the variable $\\eta$ to follow any distribution, producing trajectories of the form $X_t = a(t)X_1 + b(t)X_0 + c(t)\\eta$. We theoretically demonstrate that this construction preserves the continuity equation and maintains a training objective consistent with the marginal formulation. This flexibility enables the design of diverse probability paths using various priors, including Gaussian, Uniform, Laplace, and discrete Rademacher distributions, each offering unique geometric properties for generative flows. 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