Point-based rendering has gained much attention as an alternative to polygon-based rendering because of its simplicity and flexibility. However, current point-based rendering techniques do not provide a sufficient rendering quality for translucent materials such as human skin. In this paper, we propose a point-based rendering framework with subsurface scattering of light, which is important to create the soft and semi-translucent appearance of human skin. To accurately simulate subsurface scattering in multi-layer materials, we present splat-based diffusion to apply a linear combination of several Gaussian basis functions to each splat in object space. Compared to existing point-based approaches, our method offers a significantly improved visual quality in rendering human faces.