We develop a singular layer transmission model for continuous-variable quantum key distribution (CVQKD). In CVQKD, the transmit information is carried by continuous-variable (CV) quantum states, particularly by Gaussian random distributed position and momentum quadratures. The reliable transmission of the quadrature components over a noisy link is a cornerstone of CVQKD protocols. The proposed singular layer uses the singular value decomposition of the Gaussian quantum channel, which yields an additional degree of freedom for the phase space transmission. This additional degree of freedom can further be exploited in a multiple-access scenario. The singular layer defines the eigenchannels of the Gaussian physical link, which can be used for the simultaneous reliable transmission of multiple user data streams. Our transmission model also includes the singular interference avoider (SIA) precoding scheme. The proposed SIA precoding scheme prevents the eigenchannel interference to reach an optimal transmission over a Gaussian link. We demonstrate the results through the adaptive multicarrier quadrature division-multiuser quadrature allocation (AMQD-MQA) CVQKD multiple-access scheme. We define the singular model of AMQD-MQA and characterize the properties of the eigenchannel interference. We propose the SIA precoding of Gaussian random quadratures and the optimal decoding at the receiver. We show a random phase space constellation scheme for the Gaussian sub-channels. The singular layer transmission provides improved simultaneous transmission rates for the users with unconditional security in a multiple-access scenario, particularly in crucial low signal-to-noise ratio regimes.