to ensure png->gif maintains transparency:

ffmpeg -i '%04d.png' -gifflags +transdiff -filter_complex "split[a][b];[a]palettegen=stats_mode=single:reserve_transparent=on:transparency_color=ffffff[p];[b][p]paletteuse=new=1:dither=floyd_steinberg" output.gif

to convert gif to png

ffmpeg -i output.gif -vsync 0 frame%d.png