We characterizem-exchangeability for a large class of martingale problems on the usual space of continuous trajectories into (Rd)m, in terms of the drift and diffusion coefficients. Under some Lipschitz conditions on the coefficients, the sequence of empirical measures associated with a triangular array of exchangeable diffusions is shown to be tight. The diffusions considered here may be very strongly correlated, in which case tightness entails the existence of “random McKean–Vlasov limits”.