Forward Diff

Reverse Diff

...

(x_t^{num})_i = (x_0^{num})_i + \sigma_i^{num}(t) \epsilon \epsilon \in \mathcal{N}(0,1)

(x_t^{cat})_i = \begin{cases} m & \text{with } \mathbb{P} = 1 - \alpha_i(t) \\ (x_t^{cat})_i & \text{with } \mathbb{P} = \alpha_i(t) \end{cases}