Giant planets on short-period orbits are predicted to be inflated and eventually engulfed by their host stars. However, the detailed timescales and stages of these processes are not well known. Here, we present the discovery of three hot Jupiters (P < 10 days) orbiting evolved, intermediate-mass stars (M ⋆ ≍ 1.5 M ⊙, 2 R ⊙ < R ⋆ < 5 R ⊙). By combining TESS photometry with ground-based photometry and radial velocity measurements, we report masses and radii for these three planets of between 0.4 and 1.8 M J and 0.8 and 1.8 R J. TOI-2337b has the shortest period (P = 2.99432 ± 0.00008 days) of any planet discovered around a red giant star to date. Both TOI-4329b and TOI-2669b appear to be inflated, but TOI-2337b does not show any sign of inflation. The large radii and relatively low masses of TOI-4329b and TOI-2669b place them among the lowest density hot Jupiters currently known, while TOI-2337b is conversely one of the highest. All three planets have orbital eccentricities of below 0.2. The large spread in radii for these systems implies that planet inflation has a complex dependence on planet mass, radius, incident flux, and orbital properties. We predict that TOI-2337b has the shortest orbital decay timescale of any planet currently known, but do not detect any orbital decay in this system. Transmission spectroscopy of TOI-4329b would provide a favorable opportunity for the detection of water, carbon dioxide, and carbon monoxide features in the atmosphere of a planet orbiting an evolved star, and could yield new information about planet formation and atmospheric evolution.