The nitrogen-vacancy (NV) center in diamond is the prototype quantum defect that enables a variety of diamond-based quantum technologies. However, charge-state instability and spectral diffusion, often induced by substitutional nitrogen impurities (N_(rm C)), remain key challenges for device performance. Here, we employ first-principles density functional theory calculations to quantitatively investigate nonradiative carrier capture processes mediated by multiphonon emission at both the NV center and the N_(rm C) impurity. For relevant cases, we also compute the rates of radiative and thermal emission processes. For N_(rm C)⁰ → N_(rm C)⁻, we obtain an electron capture coefficient of 2.2 × 10⁻⁸ cm³s⁻¹ at 300 K. Both the magnitude and temperature dependence are in excellent agreement with experimentally measured capture cross sections. Electron capture at N_(rm C)⁺ is even faster, with a capture coefficient of 1.0 × 10⁻⁴ cm³s⁻¹ at 300 K. For the NV center, we find that carrier capture rates involving only the ground states of NV⁰ and NV⁻ are negligibly slow. However, capture into the excited states (NV^(0*) and NV^(-*)) is significantly faster. In particular, the capture coefficient for the hole capture process NV⁻ → NV^(0*) is as large as 1.8 × 10⁻⁷ cm³s⁻¹ and largely temperature-independent. Hole capture at NV⁻ will thus occur via nonradiative capture into an excited state of NV⁰ followed by fast radiative decay to the NV⁰ ground state. Similarly, electron capture at NV⁰ will occur via the NV⁰ → NV^(-*) → NV⁻ pathway, but with a lower nonradiative capture coefficient (2.1 × 10⁻⁹ cm³s⁻¹ at 300 K). Our calculated capture coefficients and rates provide essential information for analyzing charge-state dynamics.