Foundations and implications of science diffusion clarify how knowledge spreads within and between scientific communities and societies. This study focuses on examining the link between research funding and the citation rates of papers authored by Nobel laureates. The study uses a power-law model to investigate the connection between citation counts and the total number of papers published by Nobel laureates in physics and physiology (or medicine) in 2020, comparing research publications from funded and unfunded projects. The statistical analysis reveals that, in medicine, papers of Nobel Prizes’ scholars from funded research, mainly on problem-driven topics, tend to receive more citations than publications from unfunded research. Conversely, in physics, a hard science, highly cited papers of Nobels are more often the result of unfunded research, originated by a curiosity-driven approach. When overall papers of scholars in research fields of physics and medicine are considered, in general papers based on funded research outclass papers with unfunded research. These findings underscore the pivotal role of research funding in facilitating the spread of scientific knowledge through citations and in shaping science dynamics over time and space. Implications of science policy and optimal allocation of financial resources for greater impact of research in science and society are discussed.