During parallel flow there was a concentration gradient for albumin in all regions of the filter. The same was true for counter current flow. Why did albumin not diffuse into the dialysate?

Due to large size.

Explanation:

albumin did not diffuse into the dialysate because the size of albumin is too large for the dialysate. The purpose of dialysate is to remove toxins from the blood by the process of diffusion. The membrane through which the toxins passes are small in size so only small molecules are able to diffuse through it and no albumin diffuse through it due to large size.