Spatial self-phase modulation of a Gaussian beam in a photopolymer generated diffraction rings that propagated over unusually long distances ($\gg \text{Rayleigh}$ length) in the medium. Self-phase modulation was examined under negative, positive, and infinite wavefront curvatures ($R$) over different pathlengths. Resulting diffraction rings exhibited previously unobserved, slow dynamics, which could be directly monitored at the sample exit face. This study complements but differs fundamentally from previous ones that were predominantly carried out in thin films ($\le \text{Rayleigh}$ length) and generated static diffraction rings, which were propagated through air and imaged in the far-field. In the photopolymer, an input beam with $R<0$ generated diffraction rings with a dark center, which propagated through the medium while increasing in number, underwent filamentation, and finally transformed into a stable self-trapped beam. Diffraction rings generated under $R>0$ bore a bright center and cyclically exchanged intensity with proximal diffraction rings. Statistical analyses of self-phase modulation at $R=\infty$ identified diffraction rings, which (i) were superimposed with high order modes of a co-propagating self-trapped beam, (ii) resembled fingerprint-like rings, (iii) emerged sequentially, and (iv) possessed a bright center. Results were rationalized by combining self-phase modulation theory with the evolution of refractive index changes in the photopolymer. The findings expose a new facet of spatial self-phase modulation and the complex dynamics of diffraction rings that propagate over long distances.