2002 Other Opel Models Fuel injection

The car is a 2002 opel corsa 1.7 Litre DTI. The car starts fine. Idles fine. Pressing the gas when not in gear the car takes high RPM's fine. The problem is that when trying to drive the car, it stalls. I just bought the car and I was told it was a fuel pump problem. The problem seems to go away each time you put diesel in it. The first time was from 1/4 tank to half tank. The car ran like a champ. The next day, it was stalling again, put some fuel in it, and it ran all day no problems. The next day, same thing, and the following day as well. It seemed that each time fuel was put into the car, the problem stopped. When the car came to a full tank and I could no longer put fuel in it, I tried to clean the fuel filters and take a look at what I thought was the fuel pump under the back seat. I found that there is no pump under the back seat, just was seemed to be a large plastic filter. After cleaning everything out and replacing the fuel into the tank. It stalled again. Each time the car stalls the only thing that needs to be done to restart it is turn the key back, wait around 30 seconds and turn it over. From that point it idles just fine. No problems until you try to drive it, then, it stalls. I'm not sure where to look to solve the problem. I'm not sure if the car has a fuel pump at all and if it doesn't, how does it get fuel into the engine. If I could please have some idea of where to look or what to do it would be greatly appreciated.

Thank you for noting the info on the location of the fuel pump. New information now is that. The car only stalls when it is not at normal operating temperature. As soon as the car comes to normal temp, it can go as long and as hard as you want to take it. It stalls at about 2500 RPM only when the car is cold. Any idea's?