While diffusion models have shown promise for combinatorial optimization (CO), their inference-time scaling cost-efficiency remains relatively underexplored. Existing methods improve solution quality by increasing denoising steps, but the performance often becomes saturated quickly. This paper proposes GenSCO to systematically scale diffusion solvers by an orthogonal dimension of inference-time computation beyond denoising step expansion, i.e., search-driven generation. GenSCO takes generation as a search operator rather than a complete solving process, where each operator cycle combines solution disruption (via local search operators) and diffusion sampling, enabling iterative exploration of the learned solution space. Rather than over-refining current solutions, this paradigm encourages the model to leave local optima and explore a broader area of the solution space, ensuring a more consistent scaling effect.

Retrieval augmented generation (RAG) with large language models (LLMs) for Question Answering (QA) entails furnishing relevant context within the prompt to facilitate the LLM in answer generation. During the generation, inaccuracies or hallucinations frequently occur due to two primary factors: inadequate or distracting context in the prompts, and the inability of LLMs to effectively reason through the facts. In this paper, we investigate whether providing aligned context via a carefully selected passage sequence leads to better answer generation by the LLM for multi-hop QA. We introduce, "GenSco", a novel approach of selecting passages based on the predicted decomposition of the multi-hop questions}. The framework consists of two distinct LLMs: (i) Generator LLM, which is used for question decomposition and final answer generation; (ii) an auxiliary open-sourced LLM, used as the scorer, to semantically guide the Generator for passage selection. The generator is invoked only once for the answer generation, resulting in a cost-effective and efficient approach. We evaluate on three broadly established multi-hop question answering datasets: 2WikiMultiHop, Adversarial HotPotQA and MuSiQue and achieve an absolute gain of $15.1$ and $5.9$ points in Exact Match score with respect to the best performing baselines over MuSiQue and 2WikiMultiHop respectively.