We present AnchorDP3, a diffusion policy framework for dual-arm robotic manipulation that achieves state-of-the-art performance in highly randomized environments. AnchorDP3 integrates three key innovations: (1) Simulator-Supervised Semantic Segmentation, using rendered ground truth to explicitly segment task-critical objects within the point cloud, which provides strong affordance priors; (2) Task-Conditioned Feature Encoders, lightweight modules processing augmented point clouds per task, enabling efficient multi-task learning through a shared diffusion-based action expert; (3) Affordance-Anchored Keypose Diffusion with Full State Supervision, replacing dense trajectory prediction with sparse, geometrically meaningful action anchors, i.e., keyposes such as pre-grasp pose, grasp pose directly anchored to affordances, drastically simplifying the prediction space; the action expert is forced to predict both robot joint angles and end-effector poses simultaneously, which exploits geometric consistency to accelerate convergence and boost accuracy. Trained on large-scale, procedurally generated simulation data, AnchorDP3 achieves a 98.7% average success rate in the RoboTwin benchmark across diverse tasks under extreme randomization of objects, clutter, table height, lighting, and backgrounds. This framework, when integrated with the RoboTwin real-to-sim pipeline, has the potential to enable fully autonomous generation of deployable visuomotor policies from only scene and instruction, totally eliminating human demonstrations from learning manipulation skills.