SItoA translates ICE particle shapes to native Arnold shapes. The supported particle shapes are already documented here, but here’s a little more information about how they are translated.
||points (mode “disk”)
||box (with 0 height)
||points (mode “sphere”)
The Segment, Capsule, and Blob shapes are not supported. SItoA skips them and they are not translated into the Arnold scene source.
If you’re using world coordinates for your noise, then obviously as an object moves in global space, the noise will change. Here I’ve extracted a polygon and moved it: same shader tree that uses noise, but different noise because I’m using world coordinates.
You could keep the same noise by applying an offset equal to the translation:
Note that I’ve assumed that there’s no scaling of the noise. If there was, I’d have to multiply my offset by the same scaling.