Compared to gasoline, diesel is more susceptible to the formation of algae (mold) at the fuel/water interface. It causes clogged filters as the first symptom. The algae itself doesn't cause the clogging, it is components of the fuel after being exposed to the algae. Diesel fuel ages/degrades, and so people have gotten used to adding stabilizers to diesel fuel to prolong the life of the fuel.

This doesn't have much to do with combustion chamber cleaners such as you used on your gasoline engine. If you buy good quality fuel, you shouldn't need cleaners. If you are using cheap fuel then Techron could help the injectors in a gasoline engine. The same concepts exist with diesels, but what you are being warned about is not clogging of the injectors, but rather degraded fuel.

Lots of reading on the web on the subject. I would buy good quality and fresh fuel and not worry about it too much, unless the vehicle was being stored for a period of time, when a fuel stabilizer is a reasonable thing to add.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue