This paper introduces the Configuration Space Distance Field (CDF), a novel representation for robot manipulation planning that extends the concept of Signed Distance Fields (SDFs) from task space to robot configuration space. CDF provides a unified framework for solving problems in configuration space, enabling efficient joint angle distance queries and direct access to gradients (joint angle velocities). Unlike traditional SDFs used in task space, CDF is defined in configuration space, preserving the Euclidean property of the distance field and ensuring uniform distance spans with unit gradient magnitudes. This allows for direct gradient projection to solve inverse kinematics problems in one step, avoiding iterative methods like Gauss-Newton optimization. CDF offers several advantages, including a natural bridge between task space and configuration space, intuitive geodesics reflecting object geometry in configuration space, and the ability to inherit the merits of SDFs such as implicit structure, Boolean operations, efficient queries, and differentiability. A neural variant of CDF, called neural CDF, is also proposed, offering a compact, continuous, and analytical representation that facilitates seamless integration into learning, optimization, and control frameworks. The paper presents an efficient algorithm for computing and fusing CDFs, which can be generalized to arbitrary scenes. A corresponding neural CDF representation using multilayer perceptrons (MLPs) is introduced to achieve a compact and continuous representation while improving computation efficiency. The effectiveness of CDF is demonstrated through planar obstacle avoidance examples and with a 7-axis Franka robot in inverse kinematics and manipulation planning tasks. The results show that CDF outperforms SDFs in terms of efficiency and accuracy, particularly in solving inverse kinematics tasks through gradient projection and addressing manipulation planning challenges, leading to the generation of natural robotic motions. The paper also discusses the application of CDF in whole-body inverse kinematics and manipulation planning tasks. It demonstrates that CDF can be used to solve inverse kinematics problems without iterative procedures, leveraging the robot's kinematic structure. The results show that CDF outperforms traditional methods in terms of speed and accuracy, with the ability to compute over 700,000 valid solutions per second. Additionally, CDF is shown to be effective in manipulation planning tasks, such as the goalkeeper task and large box lifting, where it outperforms state-of-the-art methods in terms of planning time and path length. The paper concludes that CDF provides a powerful representation for robot manipulation planning, enabling efficient and accurate solutions in configuration space. It also highlights the potential of CDF in various robotic problem domains, including collision-free inverse kinematics, geometric motion planning, operation space control, multi-objective optimization, and robotic learning. The paper acknowledges the challenges posed by high-dimensional configuration spaces and limited data, but suggests that neural representations offer a trade-off between efficiency, compression, and accuracy, making them suitable for integration into other frameworks. Future work will explore the broader applicability of CDF in various robotic problem domainsThis paper introduces the Configuration Space Distance Field (CDF), a novel representation for robot manipulation planning that extends the concept of Signed Distance Fields (SDFs) from task space to robot configuration space. CDF provides a unified framework for solving problems in configuration space, enabling efficient joint angle distance queries and direct access to gradients (joint angle velocities). Unlike traditional SDFs used in task space, CDF is defined in configuration space, preserving the Euclidean property of the distance field and ensuring uniform distance spans with unit gradient magnitudes. This allows for direct gradient projection to solve inverse kinematics problems in one step, avoiding iterative methods like Gauss-Newton optimization. CDF offers several advantages, including a natural bridge between task space and configuration space, intuitive geodesics reflecting object geometry in configuration space, and the ability to inherit the merits of SDFs such as implicit structure, Boolean operations, efficient queries, and differentiability. A neural variant of CDF, called neural CDF, is also proposed, offering a compact, continuous, and analytical representation that facilitates seamless integration into learning, optimization, and control frameworks. The paper presents an efficient algorithm for computing and fusing CDFs, which can be generalized to arbitrary scenes. A corresponding neural CDF representation using multilayer perceptrons (MLPs) is introduced to achieve a compact and continuous representation while improving computation efficiency. The effectiveness of CDF is demonstrated through planar obstacle avoidance examples and with a 7-axis Franka robot in inverse kinematics and manipulation planning tasks. The results show that CDF outperforms SDFs in terms of efficiency and accuracy, particularly in solving inverse kinematics tasks through gradient projection and addressing manipulation planning challenges, leading to the generation of natural robotic motions. The paper also discusses the application of CDF in whole-body inverse kinematics and manipulation planning tasks. It demonstrates that CDF can be used to solve inverse kinematics problems without iterative procedures, leveraging the robot's kinematic structure. The results show that CDF outperforms traditional methods in terms of speed and accuracy, with the ability to compute over 700,000 valid solutions per second. Additionally, CDF is shown to be effective in manipulation planning tasks, such as the goalkeeper task and large box lifting, where it outperforms state-of-the-art methods in terms of planning time and path length. The paper concludes that CDF provides a powerful representation for robot manipulation planning, enabling efficient and accurate solutions in configuration space. It also highlights the potential of CDF in various robotic problem domains, including collision-free inverse kinematics, geometric motion planning, operation space control, multi-objective optimization, and robotic learning. The paper acknowledges the challenges posed by high-dimensional configuration spaces and limited data, but suggests that neural representations offer a trade-off between efficiency, compression, and accuracy, making them suitable for integration into other frameworks. Future work will explore the broader applicability of CDF in various robotic problem domains