Although　diffusion　prior-based　single-image　super-resolution　has　demonstrated　remarkable　reconstruction　capabilities,　its　potential　in　the　domain　of　stereo　image　super-resolution　remains　underexplored.　One　significant　challenge　lies　in　the　inherent　stochasticity　of　diffusion　models,　which　makes　it　difficult　to　ensure　that　the　generated　left　and　right　images　exhibit　high　semantic　and　texture　consistency.　This　poses　a　considerable　obstacle　to　advancing　research　in　this　field.　Therefore,　We　introduce　DiffSteISR,　a　pioneering　framework　for　reconstructing　real-world　stereo　images.　DiffSteISR　utilizes　the　powerful　prior　knowledge　embedded　in　pre-trained　text-to-image　model　to　efficiently　recover　the　lost　texture　details　in　low-resolution　stereo　images.　Specifically,　DiffSteISR　implements　a　time-aware　stereo　cross　attention　with　temperature　adapter　(TASCATA)　to　guide　the　diffusion　process,　ensuring　that　the　generated　left　and　right　views　exhibit　high　texture　consistency　thereby　reducing　disparity　error　between　the　super-resolved　images　and　the　ground　truth　(GT)　images.　Additionally,　a　stereo　omni　attention　control　network　(SOA　ControlNet)　is　proposed　to　enhance　the　consistency　of　super-resolved　images　with　GT　images　in　the　pixel,　perceptual,　and　distribution　space.　Finally,　DiffSteISR　incorporates　a　stereo　semantic　extractor　(SSE)　to　capture　unique　viewpoint　soft　semantic　information　and　shared　hard　tag　semantic　information,　thereby　effectively　improving　the　semantic　accuracy　and　consistency　of　the　generated　left　and　right　images.　Extensive　experimental　results　demonstrate　that　DiffSteISR　accurately　reconstructs　natural　and　precise　textures　from　low-resolution　stereo　images　while　maintaining　a　high　consistency　of　semantic　and　texture　between　the　left　and　right　views.