  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.
