Heatmap-based solvers have emerged as a promising paradigm for Combinatorial Optimization (CO). However, we argue that the dominant Supervised Learning (SL) training paradigm suffers from a fundamental objective mismatch: minimizing imitation loss (e.g., cross-entropy) does not guarantee solution cost minimization. We dissect this mismatch into two deficiencies: Decoder-Blindness (being oblivious to the non-differentiable decoding process) and Cost-Blindness (prioritizing structural imitation over solution quality). We empirically demonstrate that these intrinsic flaws impose a hard performance ceiling. To overcome this limitation, we propose CADO (Cost-Aware Diffusion models for Optimization), a streamlined Reinforcement Learning fine-tuning framework that formulates the diffusion denoising process as an MDP to directly optimize the post-decoded solution cost. We introduce Label-Centered Reward, which repurposes ground-truth labels as unbiased baselines rather than imitation targets, and Hybrid Fine-Tuning for parameter-efficient adaptation. CADO achieves state-of-the-art performance across diverse benchmarks, validating that objective alignment is essential for unlocking the full potential of heatmap-based solvers.

翻译：摘要：基于热力图的求解器已成为组合优化领域中一种颇具前景的范式。然而，我们认为主流的监督学习训练范式存在根本性的目标失配问题：最小化模仿损失（如交叉熵损失）并不能保证解决方案的成本最小化。我们将这种失配问题分解为两个缺陷：解码盲区（对不可微解码过程的无视）和成本盲区（将结构模仿置于解决方案质量之上）。我们通过实验证明，这些固有缺陷构成了严格的性能上限。为克服这一限制，我们提出CADO（面向优化的成本感知扩散模型），这是一种精简的强化学习微调框架，将扩散去噪过程建模为马尔可夫决策过程，以直接优化解码后的解决方案成本。我们引入了以标签为中心的奖励机制，将真实标签重新用作无偏基线而非模仿目标，并采用混合微调实现参数高效的自适应。CADO在多个基准测试中均实现了最先进的性能，从而验证了目标对齐对于充分释放热力图求解器潜力的关键作用。