We present a study of the ionizing stars associated with the diffuse ionized gas (DIG) and H II regions in the nearby spiral galaxy M33. We compare our Schmidt Hα image to the far-ultraviolet (FUV, 1520 A) image from the Ultraviolet Imaging Telescope (UIT). The Hα/FUV ratio is higher in H II regions than in the DIG, suggesting an older population of ionizing stars in the DIG. Assuming ionization equilibrium, we convert the Hα flux to the number of Lyman continuum photons NLyc. When compared to models of evolving stellar populations, the NLyc/FUV ratio in H II regions is consistent with a young burst, while the DIG ratio resembles an older burst population, or a steady state population built up by constant star formation, which is probably a more accurate description of the stellar population in the field. The UIT data is complemented with archival FUV and optical images of a small portion of the disk of M33 obtained with WFPC2 on board the Hubble Space Telescope (HST). These images overlap low- and mid-luminosity H II regions as well as DIG, so we can investigate the stellar population in these environments. Using the HST FUV and optical photometry, we assign spectral types to the stars observed in DIG and H II regions. The photometry indicates that ionizing stars are present in the DIG. We compare the predicted ionizing flux with the amount required to produce the observed Hα emission, and we find that field OB stars in the HST images can account for 40% ± 12% of the ionization of the DIG, while the stars in H II regions can provide 107% ± 26% of the Hα luminosity of the H II regions. Due to the limited coverage of the HST data, we cannot determine if stars outside the HST fields ionize some of the DIG located in the HST fields, nor can we determine if photons from stars inside the HST fields leak out of the area covered by the HST fields. We do not find any correlation between leakage of ionizing photons and Hα luminosity for the H II regions in our HST fields. However, the HST fields do not include very luminous H II regions, and it would be worthwhile to see if there is any trend at higher luminosities. If stellar photons alone are responsible for ionizing the DIG, the current results are consistent with no or few ionizing photons escaping from the galaxy.