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@@ -53,9 +53,11 @@ <h2>Contributions</h2>
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<h2>Graphical Model</h2>
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<p>Graphical model illustrating (a) DDIM inversion and (b) RF inversion. Due to nonlinearities in DM trajectory, the DDIM inverted latent <b style="color:red;">x<sub>1</sub></b> significantly deviates from the original image <b style="color:orange;">y<sub>0</sub></b>. RF inversion without controller reduces this deviation, resulting in <b style="color:purple;">x<sub>1</sub></b>. With controller, RF inversion further eliminates the reconstruction error, making <b style="color:darkcyan;">x<sub>1</sub></b> nearly identical to <b style="color:orange;">y<sub>0</sub></b>, which enhances the faithfulness.</p>
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<img class="summary-img" src="./data/graph.png" style="width:60%;"> <br>
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<h2>Overall Pipeline</h2>
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<p>
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Our method consists of three key steps: (i) Inversion – We map a (corrupted) image to a structured noise using our controlled forward ODE (8); (ii) Conditioning – We condition the reverse process on the desired text (e.g., “A bedroom”); and (iii) Generation – We then transform the structured noise into the desired image using our controlled reverse ODE (15). (Left) Inversion with rectified flows results in an atypical noise sample (<b style="color:purple;"></b>), while optimal control produces a typical noise sample (<b style="color:darkcyan;"></b>). Our method interpolates between these two processes to generate a typical structured noise (<b style="color:red;"></b>). (Right) We follow a similar strategy when converting noise back into an image.
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</p>
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<img class="summary-img" src="./data/rf-inversion-main.png" style="width:80%;"> <br>
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