Toyota Corolla 2003 2.0 D4D cold engine noise

[lassematias]

Two days ago started a weird noise with cold engine. I took today a video with outside temperature at parking facility about 7°C. 

So when I start the car, there are no additional noise, but at the second I press gas pedal and increase engine rpm, noise begins and does not stop unless I start car again or engine warms up. If I start car again, there is no noise until gas is pressed again. Today noise went completely away after 5 minutes of idling. It sounds like the noise is coming from the right side (left side on video recorded from front) or the center of the engine, which consists all the belts, oil pump, fuel pump and water pump. Also as well as injectors. 

Link to the video: https://www.youtube.com/watch?v=UxvGeUiksZo

I have tried to listen the noise but I am unable to determine where the noise is coming. Could it be something wrong with oil pump? Fuel pump? maybe injectors? AC belt is not currently installed and I do not believe its the alternator belt or wheels.

[RabButler]

Just a suggestion, but you seem to be missing a belt!

[lassematias]

2 minutes ago, RabButler said:

Just a suggestion, but you seem to be missing a belt!

Yeah I mentioned that in my first post. It is removed today due to its age and cracks everywhere and at the same time I could verify nothing over there is the cause. New belt is waiting installation. Alternator belt was changed 3 years ago at the same time with timing belt so that will stay on the car for now. Don't ask me why AC belt was not changed, I have no clue about that.