We examine the so(2, D-1) WZW model at the subcritical level -(D-3)/2. It has a singular vacuum vector at Virasoro level 2. Its decoupling constitutes an affine extension of the equation of motion of the (D+1)-dimensional conformal particle, i.e. the scalar singleton. The admissible (spectrally flowed) representations contain the singleton and its direct products, consisting of massless and massive particles in AdSD. In D=4 there exists an extended model containing both scalar and spinor singletons of sp(4). Its realization in terms of 4 symplectic-real bosons contains the spinor-oscillator constructions of the 4D singletons and their composites. We also comment on the prospects of relating gauged versions of the models to the phase-space quantization of partonic branes and higher-spin gauge theory.