Soot & PM, ash, white smoke are different things.
Soot & PM (particulate matter) is mostly carbon compound, black. Ranges from microscopic to large flakes. Good scientific studies find the microscopic stuff can get in lungs and cause cancer. Any kind of burning carbon can emit PM. Gasoline, diesel, coal, wood, propane, Nat gas, etc. Some are worse than others. Nat gas, propane and gasoline are typically low soot, but still produce some. Especially if oil gets in the combustion.
Soo & PM naturally oxidize and remove themselves from the atmosphere over time, with little long term damage. Modern diesels use very high injection pressures, controlled lean combustion, and Diesel Particulate Filters to clean up this emission. On road and off road diesel PM emissions have been controlled since the late 90's.
High soot & PM emission is characterized by rich black smoke. Hot flames with good air flow don't produce this kind of smoke.
Ash is the left over non-carbon material. It is already oxidized and is mostly inert.
White smoke is a cold flame/combustion with excess fuel to air. It is mostly unburnt hydrocarbons (HC). Usually noticeable with a wet fire, or a cold diesel start up.