<p>Phase accumulation along stochastic trajectories is a general problem in statistical physics whenever observables depend on coherent sums of phase factors. In spatially nonlinear fields, the accumulated phase becomes a nonlinear functional of Brownian motion, leading to intrinsically non-Gaussian statistics and the breakdown of variance-based descriptions. In this work, we investigate phase evolution in a quartic nonlinear field using an effective phase diffusion framework that treats the accumulated phase as a stochastic variable evolving in phase space. The quartic case is the lowest-order nonlinearity demonstrating the full recursive nature, where the phase diffusion can be solved based on the lower-order nonlinear field result. Meanwhile, it is among the lowest-order nonlinearities for which the phase-moment hierarchy does not admit closure at any finite order. Our results indicate that the phase diffusion is strongly non-Gaussian and the signal attenuation is governed by collective phase cancellation rather than variance growth. The obtained theoretical results based on the phase-space diffusion formalism naturally incorporate finite gradient field pulse width effects, and are validated by random-walk simulations. These results of the quartic field provide a general framework for analyzing nonlinear stochastic phase accumulation beyond Gaussian approximations.</p>