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A time-space traffic (TS) diagram, which presents traffic states in time-space cells with color, is an important traffic analysis and visualization tool. Despite its importance for transportation research and engineering, most TS diagrams that have already existed or are being produced are too coarse to exhibit detailed traffic dynamics due to the limitations of existing information technology and traffic infrastructure investment. To increase the resolution of a TS diagram and enable it to present ample traffic details, this paper introduces the TS diagram refinement problem and proposes a multiple linear regression-based model to solve the problem. Two tests, which attempt to increase the resolution of a TS diagram 4 and 16 times, are carried out to evaluate the performance of the proposed model. Data collected at different times, in different locations and even in different countries are employed to thoroughly evaluate the accuracy and transferability of the proposed model. Strict tests with diverse data show that the proposed model, despite its simplicity, is able to refine a TS diagram with promising accuracy and reliable transferability. The proposed refinement model will "save" widely existing TS diagrams from their blurry "faces" and enable TS diagrams to show more traffic details.