Diesel engine has higher compression ratio, hence it is subjected to very high cylinder pressures which may cause higher vibrations. In order to counter the vibrations the diesel engines have heavier flywheel than petrol engines.
Diesel engine is bigger causing it absorbing vibration, a lot of compression going on in this cycle. The principle of a flywheel is to reduce variations in the rotational speed of the shaft to which they are attached. As such they dampen an impulsive drive or load.
All internal combustion engines have speed variations and offer an impulsive drive due to their cyclic processes of induction, compression, combustion and exhaust. The extent of the speed variations is dependent on the number of cylinders and the engine configuration. A single cylinder engine exhibits the most significant difference. The momentum (stored energy) of the flywheel reduces these variations by accepting and discharging energy as required.
Diesel engines due to their higher compression ratios are more subject to crankshaft speed variation and hence require heavier (higher moment of inertia) flywheels.