Image　inpainting　methods　usually　fail　to　reconstruct　reasonable　structure　and　fine-grained　texture　simultaneously.　This　paper　handles　this　problem　from　a　novel　perspective　of　predicting　low-frequency　semantic　structural　contents　and　high-frequency　detailed　textures　respectively,　and　proposes　a　multi-frequency　probabilistic　inference　model(MPI　model)　to　predict　the　multi-frequency　information　of　missing　regions　by　estimating　the　parametric　distribution　of　multi-frequency　features　over　the　corresponding　latent　spaces.　Firstly,　in　order　to　extract　the　information　of　different　frequencies　without　any　interference,　wavelet　transform　is　utilized　to　decompose　the　input　image　into　low-frequency　subband　and　high-frequency　subbands.　Furthermore,　an　MPI　model　is　designed　to　estimate　the　underlying　multi-frequency　distribution　of　input　images.　With　this　model,　closer　approximation　to　the　true　posterior　distribution　can　be　constrained　and　maximum-likelihood　assignment　can　be　approximated.　Finally,　based　on　the　proposed　MPI　model,　a　two-path　network　consisting　of　inference　network(InferenceNet)　and　generation　network(GenerationNet)　is　trained　parallelly　to　enforce　the　consistency　of　global　structure　and　local　texture　between　the　generated　image　and　ground　truth.　We　qualitatively　and　quantitatively　compare　our　method　with　other　state-of-the-art　methods　on　Paris　StreetView,　CelebA,　CelebAMask-HQ　and　Places2　datasets.　The　results　show　the　superior　performance　of　our　method,　especially　in　the　aspects　of　realistic　texture　details　and　semantic　structural　consistency.