Before revision:  First, we introduce the reversible Heun method: a new SDE solver that is algebraically reversible -- which reduces \textit{  numerical gradient errors to almost zero, improving several test metrics by substantial margins over state-of-the-art . Moreover it requires half as many function evaluations as comparable solvers, giving up to a 1.98\times speedup.
After revision:  First, we introduce the reversible Heun method a new SDE solver that is algebraically reversible -- which reduces \textit{ numerical gradient errors to almost zero, improving several test metrics by substantial margins over state-of-the-art . Moreover it requires half as many function evaluations as comparable solvers, giving up to a 1.98\times speedup.