  Onsager's regression hypothesis makes a fundamental connection between
macroscopic transport phenomena and the average relaxation of spontaneous
microscopic fluctuations. This relaxation, however, is agnostic to odd
transport phenomena, in which fluxes run orthogonal to the gradients driving
them. To account for odd transport, we generalize the regression hypothesis,
postulating that macroscopic linear constitutive laws are, on average, obeyed
by microscopic fluctuations, whether they contribute to relaxation or not. From
this "flux hypothesis," Green-Kubo and reciprocal relations follow, elucidating
the separate roles of broken time-reversal and parity symmetries underlying
various odd transport coefficients. As an application, we derive and verify the
Green-Kubo relation for odd collective diffusion in chiral active matter, first
in an analytically-tractable model and subsequently through molecular dynamics
simulations of concentrated active spinners.
