Can cremating bodies cause black rain?

There is speculation that the mysterious black rain that Japan had a few months ago was from China cremating bodies, and in particular, mass cremations from coronavirus victims.

• 7 News: Coronavirus victims’ cremated bodies blamed on ominous black rain falling in Japan

  There are claims the sludge is the fallout from a mass incineration of coronavirus bodies in China, the aftermath of a nuclear test in North Korea or the result of fuel dumping from planes flying overhead.

  […]

  The most plausible explanation appears to be a recent fire at a plastics factory in Noda, in the neighbouring prefecture of Chiba, but this has not been confirmed either.

• Daily Mail: Incinerated coronavirus bodies, North Korean missiles, and airplane spillages among theories to explain ‘disturbing’ black rain falling over Japan

  Another Twitter user wrote: ‘Are they secretly burning the bodies of coronavirus victims?’.

• The Sun: Sinister ‘black rain’ falls over Japan sparking conspiracy theories its caused by cremated coronavirus bodies

Was this black sooty rain caused by mass cremations?