  We study transients produced by equatorial disk-like outflows from
catastrophically mass-losing binary stars with an asymptotic velocity and
energy deposition rate near the inner edge which are proportional to the binary
escape velocity v_esc. As a test case, we present the first smoothed-particle
radiation-hydrodynamics calculations of the mass loss from the outer Lagrange
point with realistic equation of state and opacities. The resulting spiral
stream becomes unbound for binary mass ratios 0.06 < q < 0.8. For synchronous
binaries with non-degenerate components, the spiral-stream arms merge at a
radius of ~10a, where a is the binary semi-major axis, and the accompanying
shock thermalizes about 10% of the kinetic power of the outflow. The
mass-losing binary outflows produce luminosities reaching up to ~10^6 L_Sun and
effective temperatures spanning 500 < T_eff < 6000 K, which is compatible with
many of the class of recently-discovered red transients such as V838 Mon and
V1309 Sco. Dust readily forms in the outflow, potentially in a catastrophic
global cooling transition. The appearance of the transient is viewing
angle-dependent due to vastly different optical depths parallel and
perpendicular to the binary plane. We predict a correlation between the peak
luminosity and the outflow velocity, which is roughly obeyed by the known red
transients. Outflows from mass-losing binaries can produce luminous (10^5
L_Sun) and cool (T_eff < 1500 K) transients lasting a year or longer, as has
potentially been detected by Spitzer surveys of nearby galaxies.
