Customers' load profiles are critical resources to support data analytics applications in modern power systems. However, there are usually insufficient historical load profiles for data analysis, due to the collection cost and data privacy issues. To address such data shortage problems, load profiles synthesis is an effective technique that provides synthetic training data for customers to build high-performance data-driven models. Nonetheless, it is still challenging to synthesize high-quality load profiles for each customer using generation models trained by the respective customer's data owing to the high heterogeneity of customer load. In this paper, we propose a novel customized load profiles synthesis method based on conditional diffusion models for heterogeneous customers. Specifically, we first convert the customized synthesis into a conditional data generation issue. We then extend traditional diffusion models to conditional diffusion models to realize conditional data generation, which can synthesize exclusive load profiles for each customer according to the customer's load characteristics and application demands. In addition, to implement conditional diffusion models, we design a noise estimation model with stacked residual layers, which improves the generation performance by using skip connections. The attention mechanism is also utilized to better extract the complex temporal dependency of load profiles. Finally, numerical case studies based on a public dataset are conducted to validate the effectiveness and superiority of the proposed method.