Heatmap regression has dominated human pose estimation due to its superior performance and strong spatial generalization. In order to conform to the form of 2D pixel arrays required by traditional neural networks, existing methods discretize the heatmap representation in space and confidence, which leads to performance degradation due to the introduction of quantization errors. This issue is significantly exacerbated as the size of the input image decreases, which is why heatmap-based methods do not perform well on low-resolution images. In this paper, we propose a novel neural representation for human pose estimation called NerPE to achieve continuous heatmap regression. Given any position within the image range, NerPE regresses the corresponding confidence scores for body joints according to the surrounding image features, which guarantees spatial and confidence continuity during training. Thanks to decoupling from spatial resolution, NerPE can output the predicted heatmaps at arbitrary resolutions during inference without retraining, making it easy to achieve sub-pixel localization precision. As long as the heatmap resolution is high enough, quantization errors are small enough to be ignored. Furthermore, we desgin a progressive coordinate decoding method, in which keypoint localization does not need to generate complete high-resolution heatmaps, so as to reduce the computational cost. The code will be released after acceptance.