We report vertical GaN-on-GaN p-n diodes with a breakdown voltage (BV) of 1.7 kV and a low differential specific ON-resistance $R_{\mathrm{\scriptscriptstyle ON}}$ of 0.55 $\text{m}\Omega \cdot \text {cm}^{2}$ with current spreading considered (or 0.4 $\text{m}\Omega \cdot \text {cm}^{2}$ using the diode bottom mesa size), resulting in a figure-of-merit ( $V_{B}^{2}/R_{\mathrm{\scriptscriptstyle ON}})$ of 5.3 GW/cm2 (or 7.2 GW/cm $^{2})$ . These devices exhibit a current swing over 14 orders of magnitude and a low ideality factor of 1.3. Temperature dependent $I$ – $V$ measurements show that the BV increases with increasing temperature, a signature of avalanche breakdown.