Most of the waste from traditional reactors is actually unspent fuel. Solid fuel rods only allow for about 1-2% energy conversion before the amount of transuranics and other contaminants built up and prevent safe operation.
The idea of the liquid fueled reactors is that you can easily change the fuel composition, ideally constantly reprocessing the fuel of contaminates, while letting the unburned fuel stay in place. This would drastically reduce the amount of waste generated (by orders of magnitude), and the 'unburnable' waste left over actually has some uses of its own (molybdenum 99 and bismuth 213).
Most of the waste is actually not the fission product itself, but everything else that is required to maintain the reactor aswell as the reactor itself.
The idea of the liquid fueled reactors is that you can easily change the fuel composition, ideally constantly reprocessing the fuel of contaminates, while letting the unburned fuel stay in place. This would drastically reduce the amount of waste generated (by orders of magnitude), and the 'unburnable' waste left over actually has some uses of its own (molybdenum 99 and bismuth 213).