Nuclear magnetic resonance (NMR) relaxation times provide detailed information about molecular motions and local chemical environments. Longitudinal T1 relaxation time is most often sensitive to relatively fast, nano- to picosecond ranges of molecular motion. Rotating frame T1ρ relaxation time reflects a much slower, micro- to millisecond range of motion, and the motional regime can be tuned by changing spin-lock field strength. Conventional methods for measuring T1 and T1ρ relaxation times are time-consuming, since experiments must be repeated many times with incremented magnetization recovery or decay delay. In this work, we introduce two novel and efficient NMR methods to correlate the T1 and T1ρ relaxation times. The first method, IR-SPICY, combines the conventional T1 inversion recovery (IR) with the single-scan T1ρ detection-based spin-lock cycle (SPICY). The second method, ultrafast (UF) IR-SPICY, allows measurement of whole two-dimensional T1-T1ρ correlation data in a single scan, in a couple of seconds, based on spatial encoding of the T1 dimension. We demonstrate the performance of the methods by studying relaxation of water in porous silica and hydrogel samples, latter acting as a model of the articular cartilage extracellular matrix. The methods allow correlating different molecular motional regimes, potentially providing unprecedented information about various chemical and biochemical systems, such as structures and fluid dynamics in porous materials, macromolecular changes in tissues, and protein dynamics. One to three orders of magnitude shortened experiment time enable the studies of changing or degrading samples. Furthermore, the single-scan approach may significantly facilitate the use of modern nuclear-spin hyperpolarization techniques to enhance the sensitivity of T1-T1ρ measurements by several orders of magnitude.