We analyze the public DESI full-shape clustering data using simulation-based priors (SBPs). Our priors are obtained by fitting normalizing flows to the distribution of EFT parameters measured from field-level simulations, themselves generated using tailored halo occupation distribution (HOD) models for each tracer. Incorporating SBPs in a power spectrum analysis significantly enhances $\Lambda$CDM cosmological parameter constraints; in combination with BAO information from DESI DR2 and a BBN prior on the baryon density, we find the matter density parameter ${\Omega }_m=0.2987\pm 0.0066$, the Hubble constant $H_0=68.80\pm 0.35km{s}^{-1}{Mpc}^{-1}$, and the mass fluctuation amplitude ${\sigma }_8=0.766\pm 0.015$ (or the lensing parameter $S_8=0.764\pm 0.018$), which are $1\%$, $40\%$ and $50\%$ stronger than the baseline results, though with a notable downwards shift in ${\sigma }_8$, . The SBPs also have a significant impact in extended models, with the dark energy figure-of-merit improving by $70\%$ ($20\%$) in a $w_0{w}_a$CDM analysis when combining with the CMB (and supernovae). In the SBP analysis, we do not find statistically significant evidence for dynamical dark energy: the equation of state parameters are consistent with a cosmological constant within $2.2\sigma$ ($1.4\sigma$) in analyses without (with) supernovae. The neutrino mass constraints are also enhanced, with the $95\%$ limits $M_{\nu }<0.073eV$ and $M_{\nu }<0.090eV$ in $\Lambda$CDM and $w_0{w}_a$CDM respectively. The latter is the strongest constraint obtained to date and reinforces the preference for the normal neutrino mass hierarchy, regardless of the background dynamics. While our results are sensitive to HOD modeling assumptions, they clearly demonstrate that the inclusion of small-scale information can significantly sharpen cosmological parameter constraints.