This paper discusses a class of multi‐term Caputo–Katugampola fractional delay integral diffusion equations (MCKFIDEs, for short) in Hilbert spaces. A iterative scheme in interval corresponding to the MCKFIDE is introduced by using a temporally semi‐discrete method based on the backward Euler difference scheme, i.e., Rothe's method. First, we apply the iterative scheme and the ‐accretivity of operator to establish existence, uniqueness, and a priori estimate for strong solutions to an approximate problem. Based on this result, we obtain existence, regularity of the strong solution for MCKFIDEs on interval or the maximum interval . Then, we also prove that the strong solution is unique if and only if the delay boundary condition is unique on . Finally, two examples are given to illustrate the main results.