  It is always a challenge for recommender systems to give high-quality
outcomes to cold-start users. One potential solution to alleviate the data
sparsity problem for cold-start users in the target domain is to add data from
the auxiliary domain. Finding a proper way to extract knowledge from an
auxiliary domain and transfer it into a target domain is one of the main
objectives for cross-domain recommendation (CDR) research. Among the existing
methods, mapping approach is a popular one to implement cross-domain
recommendation models (CDRs). For models of this type, a mapping module plays
the role of transforming data from one domain to another. It primarily
determines the performance of mapping approach CDRs. Recently, diffusion
probability models (DPMs) have achieved impressive success for image synthesis
related tasks. They involve recovering images from noise-added samples, which
can be viewed as a data transformation process with outstanding performance. To
further enhance the performance of CDRs, we first reveal the potential
connection between DPMs and mapping modules of CDRs, and then propose a novel
CDR model named Diffusion Cross-domain Recommendation (DiffCDR). More
specifically, we first adopt the theory of DPM and design a Diffusion Module
(DIM), which generates user's embedding in target domain. To reduce the
negative impact of randomness introduced in DIM and improve the stability, we
employ an Alignment Module to produce the aligned user embeddings. In addition,
we consider the label data of the target domain and form the task-oriented loss
function, which enables our DiffCDR to adapt to specific tasks. By conducting
extensive experiments on datasets collected from reality, we demonstrate the
effectiveness and adaptability of DiffCDR to outperform baseline models on
various CDR tasks in both cold-start and warm-start scenarios.
