Diffusion models have shown impressive sample generation capabilities across various domains. However, current methods are still lacking in human-understandable explanations and interpretable control: (1) they do not provide a probabilistic framework for systematic interpretation. For example, when tasked with generating an image of a "Nighthawk", they cannot quantify the probability of specific concepts (e.g., "black bill" and "brown crown" usually seen in Nighthawks) or verify whether the generated concepts align with the instruction. This limits explanations of the generative process; (2) they do not naturally support control mechanisms based on concept probabilities, such as correcting errors (e.g., correcting "black crown" to "brown crown" in a generated "Nighthawk" image) or performing imputations using these concepts, therefore falling short in interpretable editing capabilities. To address these limitations, we propose Energy-based Conceptual Diffusion Models (ECDMs). ECDMs integrate diffusion models and Concept Bottleneck Models (CBMs) within the framework of Energy-Based Models to provide unified interpretations. Unlike conventional CBMs, which are typically discriminative, our approach extends CBMs to the generative process. ECDMs use a set of energy networks and pretrained diffusion models to define the joint energy estimation of the input instructions, concept vectors, and generated images. This unified framework enables concept-based generation, interpretation, debugging, intervention, and imputation through conditional probabilities derived from energy estimates. Our experiments on various real-world datasets demonstrate that ECDMs offer both strong generative performance and rich concept-based interpretability.