Solving storage problem: where objects must be accurately placed into containers with precise orientations and positions, presents a distinct challenge that extends beyond traditional rearrangement tasks. These challenges are primarily due to the need for fine-grained 6D manipulation and the inherent multi-modality of solution spaces, where multiple viable goal configurations exist for the same storage container. We present a novel Diffusion-based Affordance Prediction (DAP) pipeline for the multi-modal object storage problem. DAP leverages a two-step approach, initially identifying a placeable region on the container and then precisely computing the relative pose between the object and that region. Existing methods either struggle with multi-modality issues or computation-intensive training. Our experiments demonstrate DAP's superior performance and training efficiency over the current state-of-the-art RPDiff, achieving remarkable results on the RPDiff benchmark. Additionally, our experiments showcase DAP's data efficiency in real-world applications, an advancement over existing simulation-driven approaches. Our contribution fills a gap in robotic manipulation research by offering a solution that is both computationally efficient and capable of handling real-world variability. Code and supplementary material can be found at: https://github.com/changhaonan/DPS.git.