Molecules with three or more nuclei of nonzero spin exist as discrete spin isomers whose interconversion in the gas phase is generally considered improbable. We have studied the interconversion process in ethylene by creating a sample depleted in the B2u nuclear spin isomer. The separation was achieved through spatial drift of this isomer induced by resonant absorption of narrow-band infrared light. Evolution of the depleted sample revealed conversion between B2u and B3u isomers at a rate linearly proportional to pressure, with a rate constant of 5.5 (+/-0.8) x 10(-4) s(-1) torr(-1). However, almost no change was observed in the Ag isomer populations. The results suggest a spin conversion mechanism in C2H4 via quantum relaxation within the same inversion symmetry.