We present a large-scale study of diffuse X-ray emission in the nearby massive stellar association Cygnus OB2 as part of the Chandra Cygnus OB2 Legacy Program. We used 40 Chandra X-ray ACIS-I observations covering $sim$1.0 deg$^2$. After removing 7924 point-like sources detected in our survey, background-corrected X-ray emission, the adaptive smoothing reveals large-scale diffuse X-ray emission. Diffuse emission was detected in the sub-bands Soft [0.5 : 1.2] and Medium [1.2 : 2.5], and marginally in the Hard [2.5 : 7.0] keV band. From X-ray spectral analysis of stacked spectra we compute a total [0.5 : 7.0 keV] diffuse X-ray luminosity of L$_{rm x}^{rm diff}approx$4.2$times$10$^{rm 34}$ erg s$^{-1}$, characterized with plasma temperature components at kT$approx$ 0.11, 0.40 and 1.18 keV, respectively. The HI absorption column density corresponding to these temperatures has a distribution consistent with N$_{rm H}$ = 0.43, 0.80 and 1.39 $times$10$^{22}$ cm$^{-2}$. The extended medium band energy emission likely arises from O-type stellar winds thermalized by wind-wind collisions in the most populated regions of the association, while the soft band emission probably arises from less energetic termination shocks against the surrounding Interstellar-Medium. Super-soft and Soft diffuse emission appears more widely dispersed and intense than the medium band emission. The diffuse X-ray emission is generally spatially coincident with low-extinction regions that we attribute to the ubiquitous influence of powerful stellar winds from massive stars and their interaction with the local Interstellar-Medium. Diffuse X-ray emission is volume-filling, rather than edge-brightened, oppositely to other star-forming regions. We reveal the first observational evidence of X-ray haloes around some evolved massive stars.
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