Sadly there is no such thing! While refered to a silent, actually all generators make a noise. People use the term "Silent Diesel generator" to refer to a generator that is housed in a type of acoustic enclosure. As standard, these are not that quiet! You can of course make them as quiet as you want to, however with that comes not only considerably cost, but also an increase in size!
A typical diesel generator that has no acoustic protection is very noisy! Typically 110bBA@1m - that is like a jet taking off nearby! The noise comes form the exuast and also the frame of the machine. It is generated when the diesel engine combustion - an explosion - happens in the engines cylinders. A silent type generator helps reduce this noise to a level that is more appropriate for the local enviroment.
Silent diesel generators have several benefits, all of which are significant: quieter operation, weather protection, mechanical protection and visual improvement. All this comes at a price, so silent diesel generators are more expensive, but isn't everything better more expensive?
There shouldn't be any difference - the components are the same. The silent diesel generator is enclosed and therefore better protected from the weather, but badly designed units can suffer due to increased heat in the unit which can cause problems.
Noise levels are always quoted as an average at a specific distance, in free field conditions. What does this mean? Well, it means the measurement has been take in an acoustic chamber - so no echos from any direction. That means in your application the unit will probably be considerably noiser than it may appear on the specification sheet. The average figure means that the unit has several measurments taken from different directions and the overall noise averaged - again this may bean one side of the unit is much noisier than the others!
Finally the distance - probably the easiest part to understand. The noise is measured at a distance, some use 1m, some 3m, some 7m, some 11m. This may not seem like a lot, but the noise measurement from 7m is around 11dBA lower - thats almost 4 times quieter! Its therefore really important you look at the levels and the distance to make an informed desision.
Now that is a good question! ultimately if you need something that you can talk next to, you are going to need a silent type diesel generator!
Investigate and look! Do you want to pay the price premium for a silent generator? This Consumer Reports article on small silent Inverter generators ranks a few popular models. Search and find other information on the units you are interested in and make an informed desision. These generators are only really available up to 5000w, so if you need something bigger a Perkins Diesel Generator or Baudouin Diesel Generator