Cause of flat/increasing TV vs guidance at large w under Tau-leaping

Determine whether the observed flat or increasing region in the curve of total variation distance versus guidance strength w, for the 1D masked discrete diffusion reverse dynamics simulated via Tau-leaping, is primarily caused by the sharp transition of the reverse sampling dynamics at large w that makes the Tau-leaping scheme less efficient and less stable.

Background

The authors empirically plot the total variation distance as a function of guidance strength w for 1D guided masked discrete diffusion and note agreement with theory at small w but a flattening or slight increase at large w. They attribute this behavior to numerical issues rather than theoretical disagreement.

Given their theoretical result that the decay rate of total variation along the reverse dynamics depends double-exponentially on w for large w, they conjecture that Tau-leaping struggles with the resulting sharp temporal transition, leading to inefficiency and instability. Confirming this causal mechanism would clarify practical limitations and inform more robust numerical strategies.