In this talk I will present a new “anomalous regularisation” result for solutions of the stochastic transport equation $\partial_t \rho + \circ \partial_t W \cdot \nabla \rho = 0$ on $\mathbb{R}^d$, where W is a Gaussian, homogeneous, isotropic noise with $\alpha$-H\”older space regularity and compressibility ratio $\wp < \frac{d}{4\alpha^2}$. The proof is obtained by studying the local behaviour around the origin of solutions to a degenerate parabolic PDE in non-divergence form, which is of independent interest. Based on joint work with Theodore Drivas and Lucio Galeati.