As Bernanke says in 'Essays on the Great Depression',
Second, for reasons that were largely historical, political, and philosophical rather than purely economic, some governments responded to the crises of the early 1930s by quickly abandoning the gold standard, while others chose to remain on gold despite adverse conditions. Countries that left gold were able to reflate their money supplies and price levels, and did so after some delay; countries remaining on gold were forced into further deflation. To an overwhelming degree, the evidence shows that countries that left the gold standard recovered from the Depression more quickly than countries that remained on gold. Indeed, no country exhibited significant economic recovery while remaining on the gold standard. The strong dependence of the rate of recovery on the choice of exchange-rate regime is further, powerful evidence for the importance of monetary factors.
This raises the question of whether the mechanism was just a relaxation of the constraint on monetary expansion or something that came from changes in relative prices.