Your first part of the statement is correct -- that is called the "forward process" and it is only needed at training time.

Yes, the encoder in DDIM is basically adding a predicted-noise to travel back to x_T -- it's more like the "reverse of the reverse process", but we can't really call it the "forward process", can we? For example, the true "forward process" is almost entire random and you can skip to any x_t by re-parameterization. This isn't true for DDIM's "reverse of the reverse process" -- it must be sequential and deterministic.