What allows WFIRST to have similar resolution to Hubble over a 100x larger solid angle? In the video linked in the Space.com article What Would It Mean for Astronomers If the WFIRST Space Telescope Is Killed?, (available in YouTube as WFIRST: The Best of Both Worlds) after 02:00 NASA astrophysicist Neil Gehrels says of WFIRST:


  It has the same image precision and power as the Hubble Space Telescope, but with one-hundred times the area of sky that is used.


Looking at the crude drawing on this NASA page shows only a Cassegrain-like geometry, but there must be additional goodies to obtain a similar resolution with a 10x wider field. Does it have three, four, or five mirrors like the E-ELT or the LSST (cf. What is a quaternary mirror and why does the E-ELT need one? and answers therein) or corrector lenses? What is the magic sauce that makes this possible, and is there at least a schematic diagram of the optics somewhere?



above: From NASA.
The ultimate resolution of a telescope depends upon its diameter. The larger the telescope aperture, the finer the resolution.
Hubble and WFIRST are both the same diameter 2.4m so they both have the same theoretical resolution.
However the image quality on any telescope degrades the further you are away from the optical axis. In WFIRST there is a 3rd mirror that corrects for these inherent distortions for a much wider field of view.
The last factor is the improvement in detector technology. The individual pixels are smaller, smaller gaps, and there chips are much larger. Also WFIRST has mosaic of these  CCD chips to cover the larger corrected field of view.
The paper Optical Design of the WFIRST-AFTA Wide-Field Instrument (Pasquale et al. 2014, Proc. SPIE-OSA Vol. 9293, 929305) discusses the design of the optical path (cycle #4). In addition to a small figure adjustment to the primary, the figures of the secondary and a tertiary mirror are optimized to provide high resolution over a much wider field than the HST. This design also provides a pupil at which filters can be located as well as an intermediate focus (1:1 with the final focus) as shown below.

The basic optical design is decidedly simple for fabrication, integration and test purposes. This approach begins with the base optical design; all three powered mirrors are optically co-axial and simple conics. We considered more complicated designs, including the use of tilted and de-centered mirrors and Zernike and/or anamorphic surface figures.[2,3] TMA designs are widely preferred for high A*Omega telescopes such as JWST and ATLAST.
The primary mirror, referred to here as Telescope mirror 1 (T1), is a fast f/1.2 primary with a linear central obscuration of 31%. It is a light-weighted mirror using a hollow honeycomb core. T1 and Telescope mirror 2 (T2) together form an ~f/8, intermediate focus. This focus is uncorrected, with a large caustic image and strongly curved image surface. You will note the off-axis field bias (seen in Figure 1); this is typical in all TMA systems.
Within the instrument, Mirror 3 (M3) is almost a 1:1 magnification relay of the intermediate image to the focal plane. Working in concert with T1 &amp; T2, these 3 powered mirrors form the large corrected field of the TMA. A pupil is formed between M3 and the focal plane. With a diameter of approximately 100mm, the pupil allows for the insertion of bandpass filters and spectral dispersion elements via an element wheel. Finally, in order to package the system into the volume constraints, two fold mirrors were used.