We classify inflationary models into three types: (1) the Einstein gravity theory with inflation scalar field, (2) modified gravity theories with ordinary matter fluid, and (3) the hybrid of these two models. Extended inflation and soft inflation belong to the third class. We then analyze the details of soft inflationary models, which have two scalar fields; one is the standard inflation, whose potential is exponentially coupled to the other field. We consider satisfaction of the inflationary constraints. New inflation works well, with the coupling constant near the values allowed by grand unified theories. For chaotic inflation with a massive inflation, we find successful inflation without fine-tuning of the coupling constant or initial data.