I'm afraid that diesels do have catalytic converters. They are not as complicated as those on petrol cars, but nevertheless they are still catalytic converters. Diesels are required to have a two-way catalytic converter that catalyses the oxidation of partially burned hydrocarbons (CHx) and carbon monoxide (CO) into water (H2O) and carbon dioxide (CO2). Diesels always have plenty of excess oxygen in the exhaust (except at full throttle, but then there is almost nothing to catalyse).
Because there is no need to tune the fuel injection to ensure excess oxygen in the exhaust, there is no need for lambda probes, which measure the oxygen content in petrol car exhausts.
In the last few years, diesels have also had to have Diesel Particulate Filters installed. These could be viewed as a box to collect soot, although it is a bit more complicated than that. This is in addition to the catalytic converter.