We discuss under which conditions multi-field cold and warm inflationary models with canonical kinetic energy terms are compatible with the swampland conjectures about the emergence of de Sitter solutions in string theory. We find that under quite general con-ditions the slow-roll conditions for multi-field cold inflation are at odds with the swampland conjectures for an arbitrary number of scalar fields driving inflation. However, slow-roll con-ditions can be reconciled with the swampland conjectures in the strong dissipative regime of warm inflation.
