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 conditions 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 conditions can be reconciled with the swampland conjectures
in the strong dissipative regime of warm inflation.