Stipple patterns, point sets whose local density tracks a target image, are traditionally produced by per-density iterative optimizers, which are slow, non-differentiable, and must be re-run from scratch for each new target. Learned alternatives have so far addressed only unconditional point generation; capacity-constrained, image-conditioned stippling has remained out of reach. We present the first diffusion-based sampler that simultaneously satisfies a learned local point-distribution prior and a continuous, image-defined capacity constraint at inference. The method is a ControlNet branch built on top of an optimal-transport-grid point-set diffusion baseline, conditioned on the target density map and a high-resolution image. Two design choices make the combination tractable: training and inference are restricted to the late-stage denoising regime, initialized from a density-weighted rejection sample, and the standard zero-convolution injection is replaced with a sigmoid-gated 1x1 projection that preserves the base model's blue-noise structure under hard density signals. A single trained checkpoint accepts arbitrary target densities at inference, generalizes to point budgets that were not seen during training, and produces stipples in time nearly independent of the output point count. On the Icons-50 benchmark, our learned sampler reaches parity with per-density-optimized baselines on every reported metric while remaining differentiable end-to-end.

翻译：点画图案（其局部密度追踪目标图像的点集）传统上通过逐密度迭代优化器生成，这类方法速度慢、不可微分，且每处理新目标图像时需从头重新运行。目前已提出的学习型替代方案仅能处理无条件点生成，而受容量约束、以图像为条件的点画生成仍无法实现。我们提出首个基于扩散的采样器，可在推理阶段同时满足学习到的局部点分布先验和连续的、由图像定义的容量约束。该方法构建于最优传输网格点集扩散基线之上的ControlNet分支，以目标密度图和高分辨率图像为条件。两项设计选择使该组合方案切实可行：训练与推理限定于从密度加权拒绝采样初始化的后期去噪阶段，并将标准零卷积注入替换为能保持基础模型在强密度信号下蓝噪声结构的sigmoid门控1×1投影。单个训练好的检查点在推理时可接受任意目标密度，泛化至训练中未见过的点数预算，且生成点画所需时间几乎与输出点数无关。在Icons-50基准测试中，我们的学习型采样器在全部报告指标上均达到与逐密度优化基线相当的水平，同时保持端到端可微分性。