The majority of solid-state deformation and transformation processes involve coupled displacive-diffusional mechanisms, of which a detailed atomic picture does not exist. We present here a complete atomistic description of one such process by which an extended edge dislocation in face-centered-cubic (fcc) metals may climb at finite temperature under supersaturation of vacancies. We employ an approach called ``diffusive molecular dynamics,'' which can capture the diffusional time scale while maintaining atomic resolution by coarse graining over atomic vibrations and evolving atomic density clouds. We find that, unlike the Thomson-Balluffi mechanism, if simultaneous displacive and diffusive events are allowed, a coupled displacive-diffusional pathway exists for extended double jog formation. Along this pathway, the activation energy is lower than the previous theoretical predictions and on par with the experimental observations.