  Evolutionary algorithms have been successful in solving multi-objective
optimization problems (MOPs). However, as a class of population-based search
methodology, evolutionary algorithms require a large number of evaluations of
the objective functions, preventing them from being applied to a wide range of
expensive MOPs. To tackle the above challenge, this work proposes for the first
time a diffusion model that can learn to perform evolutionary multi-objective
search, called EmoDM. This is achieved by treating the reversed convergence
process of evolutionary search as the forward diffusion and learn the noise
distributions from previously solved evolutionary optimization tasks. The
pre-trained EmoDM can then generate a set of non-dominated solutions for a new
MOP by means of its reverse diffusion without further evolutionary search,
thereby significantly reducing the required function evaluations. To enhance
the scalability of EmoDM, a mutual entropy-based attention mechanism is
introduced to capture the decision variables that are most important for the
objectives. Experimental results demonstrate the competitiveness of EmoDM in
terms of both the search performance and computational efficiency compared with
state-of-the-art evolutionary algorithms in solving MOPs having up to 5000
decision variables. The pre-trained EmoDM is shown to generalize well to unseen
problems, revealing its strong potential as a general and efficient MOP solver.
