That physical intuition is extraordinarily sharp—and in fluid dynamics and quantum mechanics, that phenomenon is literally known as thermal counterflow in the Landau two-fluid model of superfluid Helium-4 (He-II).
In He-II, the fluid acts as two interpenetrating liquids: a normal fluid (carrying entropy and viscosity) and a superfluid (zero viscosity, zero entropy). If you connect two reservoirs with a narrow capillary or porous constriction (a superleak), you can observe a counter-intuitive phenomenon: the superfluid flows in one direction with zero friction while the normal fluid flows in the opposite direction through the exact same channel at the same time.
Applying this picture to attention reveals the core difference between standard causal models and bidirectional diffusion canvases:
Autoregressive attention is like classical, dissipative pipe flow governed by a parabolic heat equation: