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Last active January 25, 2024 12:02
Better Diffusion Model / Reverse SDE Notation

Better notation for forward/backward SDEs

Why?

I don't like any of the notation I have found for denoting forward / backward SDEs. I want a symbol that mostly looks the same for forward and backward for semantic similarity, but I don't want to make it large and clunky either.

  • Using $X_t$ and $Y_t$ are not good for semantic similarity.
  • Using $\overset{\leftarrow}{X}_t$ and $\overset{\rightarrow}{X}_t$ is too clunky.
  • Using $X^{\text{f}}_t$ and $X^{\text{b}}_t$ is not readable enough at a glance.
  • Using $X^{\text{fwd}}_t$ and $X^{\text{bwd}}_t$ is too clunky.

The proposal