  Feasible solutions are crucial for Integer Programming (IP) since they can
substantially speed up the solving process. In many applications, similar IP
instances often exhibit similar structures and shared solution distributions,
which can be potentially modeled by deep learning methods. Unfortunately,
existing deep-learning-based algorithms, such as Neural Diving and
Predict-and-search framework, are limited to generating only partial feasible
solutions, and they must rely on solvers like SCIP and Gurobi to complete the
solutions for a given IP problem. In this paper, we propose a novel framework
that generates complete feasible solutions end-to-end. Our framework leverages
contrastive learning to characterize the relationship between IP instances and
solutions, and learns latent embeddings for both IP instances and their
solutions. Further, the framework employs diffusion models to learn the
distribution of solution embeddings conditioned on IP representations, with a
dedicated guided sampling strategy that accounts for both constraints and
objectives. We empirically evaluate our framework on four typical datasets of
IP problems, and show that it effectively generates complete feasible solutions
with a high probability (> 89.7 \%) without the reliance of Solvers and the
quality of solutions is comparable to the best heuristic solutions from Gurobi.
Furthermore, by integrating our method's sampled partial solutions with the
CompleteSol heuristic from SCIP, the resulting feasible solutions outperform
those from state-of-the-art methods across all datasets, exhibiting a 3.7 to
33.7\% improvement in the gap to optimal values, and maintaining a feasible
ratio of over 99.7\% for all datasets.
