Exploring Low-Dimensional Subspace in Diffusion Models for Controllable Image Editing

We appreciate the reviewer's constructive feedback that helps improve the quality of our work. Below, we address the reviewer's major concerns and clarify potential misunderstandings in some parts of our work. And we will incooperate those valuable points into our final version.

Q1: Literature review of related works.
(L189-190) I think ... such as Blended diffusion.

A1:

1. First, a detailed discussion of related works is provided in Appendix B for space limitations. There, we thoroughly review the existing literature on (1) semantic latent spaces of diffusion models, (2) global image editing in unconditional diffusion models, and (3) local/global image editing in conditional diffusion models.
2. Several existing methods address local editing in conditional diffusion models, such as CLIP-guided diffusion in BlendedDiffusion and classifier-free guidance diffusion in SEGA [22]. However, local editing remains challenging for purely unconditional diffusion models. Thanks the reviewer. We will clarify this point in lines 189-190 and include BlendedDiffusion in related works.

Q2: Lack of baselines and comparisons...

A2: Thanks to the suggestions, we conduct comparisons with BlendedDiffusion and NoiseCLR [1], with details in Q&A 1 of the global response.

Q3: Lack of ablation studies; null space projection

A3: We showed the role of nullspace projection in Fig. 8 in Appendix, and refer the summary of ablation studies to Q&A 2 in the global response.

Q4: Uninterpretable semantic change…

A4: These are great points, but we want to give further clarification:

1. Unsupervised vs supervised edit. Unsupervised edit finds edit directions without any label or text prompt such as Pullback [25] and NoiseCLR, while supervised edit utilizes labels or text supervision such as BlendedDiffusion and SEGA [22]. Both are important research directions. Our method mostly focuses on unsupervised edit (Fig. 1 and 5), but can be extended to supervised edit with a target text prompt as shown in Fig. 4(b).
2. Interpretation of semantic changes. Even in unsupervised edit, the semantic change directions can be interpreted only after being identified. For example, in Fig. 5, these directions indeed have semantic meanings: colors are changed from white to red, tower architecture are changed from simple to complex. We will make the descriptions more concrete.

Q5: Misunderstandings on our paper.

1. The actual results are not from PMP but from DDIM
2. (L80) The $x_0$ sampled from $p_{data}$ might need to be the input to get $x_t$, not the output of the posterior distribution
3. (L157) The proposed method is not one-step editing...
4. (L159-165) Are the three properties...
5. What are the undirected t2i edit...

A5: We want to clarify these misunderstandings:

1. PMP and DDIM. We use PMP at time step $t$ to find the direction $v_p$ and edit $x_t$ as $x_t + \lambda v_p$. In contrast, DDIM-Inv is used to get $x_t$ from $x_0$, and DDIM is to generate the edited image by denoising $x_t + \lambda v_p$. We use both PMP and DDIM, whereas PMP takes the most important role in finding the edit direction $v_p$.
2. Clarification on L80. $\mathbb{E}_{x_0 \sim p\_{data}(x)}[x_0|x_t]$ is the expectation of $x_0$ given the observed $x_t$ and the prior distribution $p\_{data}(x)$. Its output is indeed not $x_0$.
3. One-step editing. In [25], “one step” means only changing $x_t$ at one timestep $t$ for image editing. In comparison, as mentioned by reviewer 9wnQ, NoiseCLR requires edits across multiple timesteps.
4. Experimental verification of three properties. These properties have been demonstrated in Fig. 1 (b,c,d) and discussed in L 64 - 69. Particularly, in Fig. 1$c$, the disentangled editing directions are composable: linear combination of two editing directions result in changes of two attributes simultaneously.
5. Undirected and text-directed T2I edit. Suppose T2I diffusion models generate an image based on text prompt $c_o$.
   • In Undirected T2I edit, image is edited without additional editing prompt for the target edit direction.
   • In Directed T2I edit, an extra editing prompt $c_e$ is provided. So it is called “text-directed T2I edit”.

Q6: For Fig. 2:

1. Whether the results be generalized to more data samples and prompts
2. Define rank ratio and interpret Eq. 10
3. Why use the norm ratio

A6: Thanks for raising these points.

1. We test 15 more text prompts. As shown in Fig. F of the global response PDF. Results demonstrate the generalizability of more prompts and initial noises.
2. The rank ratio is defined in Line 144, which is the ratio between the numerical rank and the ambient dimension $d$. Eq.10 can be interpreted as finding the smallest $r$ such that: compared to the top-$r$ largest singular values of the given Jacobian, the remaining singular values are smaller than a threshold and can be neglected.
3. The norm ratio $||l - f||_2/||l|_2$ measures relative distance to better reflect linearlity. If $l$ and $f$ are apart from each other but $||l||_2$ and $||f||_2$ are too small, the absolute norm differences $||l - f||_2$ may be too small to reflect violations of linearity, but the norm ratio can.

Q7: (L37) What are the various other unexplored aspects?

A7: Specifically, these aspects include but not limited to (1) whether diffusion models have semantic spaces; (2) what features lie in the semantic spaces; (3) theoretically justify those semantic features; (4) utilize those features unsupervised local edit in unconditional diffusion models. In this work, we looked into all these aspects and proposed LOCO edit that tackles many of the questions raised. We will make the discussion clearer.

[1] Yusuf et al., "Noiseclr: A contrastive learning approach for unsupervised discovery of interpretable directions in diffusion models." CVPR 2024.

Dear Reviewer hJrH,

We have worked diligently to resolve your concerns.

As the rebuttal period comes to an end, please do not hesitate to contact us if you have any last-minute questions or require further clarification.

Best regards,

The Authors

Dear reviewer,

Thanks for the positive response and we appreciate your acknowledgment of our responses in addressing the existing problems.

For the proposed precise point: (1) We have tested transferring edit direction from “white to red” to flowers in other colors including blue, pink, and orange. We saw the colors change to darker blue, darker pink, and darker orange. Considering the effects of transferring, the edit direction can be described as “darker color”, which is semantically meaningful for flowers in general. (2) To further discuss the point, when transferring “enlarging eyes” to images of a person wearing sunglasses, only the details of the sunglasses are changed which is hard to notice. This is because “enlarging eyes” is not semantically meaningful for people wearing sunglasses. (3) Such edge cases are interesting, but since we consider practical editing scenarios where the edit directions are semantically meaningful, we do not present them in the paper. Besides, we can not show additional figures, but we will add those in our revision to make the discussion more complete.

Thanks for the question and hope we have further addressed your concerns. We are happy to answer any other questions.

Best Regards,

Authors

We thank the reviewer for constructive feedback and interesting questions. During rebuttal, we address the reviewer’s concerns on the experiments and other questions as follows.

Q1: The qualitative resultes are not quite the best... up-to-date with the current state of image editing.

A1: Thank the reviewer for pointing out the interesting works NoiseCLR and Concept sliders. We have looked into them and will cite and add discussions on NoiseCLR and Concept sliders in the revised manuscript. Besides, based on the reviewer's suggestion, we conducted more qualitative and quantitative baseline comparisons with NoiseCLR. Moreover, we extend both qualitative and quantitative results per the reviewer's suggestion. We refer detailed results and discussion to Q&A 1 of the global response.

Q2: Since the linearity and low-rankness properties are more apparent in the middle time-steps, applying more global edits... would be difficult since more coarse level features are constructed in the earlier timesteps of denoising...are edited as well.

A2: Thanks for raising this point here, and we would like to discuss further.

1. For coarse features that are controlled in early time steps close to random noise, LOCO is not guaranteed to disentangle these features in the high-rank space. This is closely related to our method is principled in the low-rank subspace of diffusion models in the middle time steps, and hence we mainly focus on unsupervised precise local edit.
2. It would be interesting to non-trivially model the space at those high-rank timepoints, maybe taken inspiration from works such as NoiseCLR. Our current focus is to study the low-rank subspaces in diffusion models and leave the understanding of semantics in high-rank spaces to be explored in future studies.

Q3: I am quite surprised that an edit at a single timestep has enough effect to edit the image. For instance, [1,2] require over multiple timesteps. Is there an intuition for why this edit at a single timestep has enough causal effect?

A3: Thanks for the interesting question and we try to provide possible intuitions.

1. From the perspective of method principles, LOCO initiates from the local linearity of PMP, and tries to find directions that lead to the largest changes in the posterior mean. Under the assumption of local linearity within the low-rank semantic subspace, such identified direction $v$ can achieve one step edit with appropriate edit strength. Following the intuition above, the one-step edit ability is experimentally verified.
2. In contrast, NoiseCLR optimizes a conditional variable representing specific features to be used in classifier-free guidance, and Concept sliders use LoRA to finetune a Slider that steers the generation to be more aligned with using conditional variable $c+$ instead of $c-$. Such indirect optimization and finetuning based on conditional variables may benefit from multiple timesteps to achieve faster convergence in optimization and better performance in editing.

Q4: For more open-domain diffusion models like Stable Diffusion, can the edit direction be applied to another subject? For instance, in Figure 1, you transfer human opening eyes to different images. Would this transfer to other domains, such as an animal?

A4: Thanks for the interesting question, and we would like to discuss it further.

1. The transferability has a high success rate for unconditional diffusion, which matches our theoretical analysis for unconditional diffusion models. However, it’s currently hard to transfer edit directions for more open-domain T2I diffusion models as we have experimented.
2. It is potentially because the feature space of these diffusion models is more complicated correlating with various text prompts. Such feature space does not align with the assumptions in the theoretical analysis for unconditional diffusion models.
3. The modeling of feature space in T2I diffusion models is still an open and interesting question in the area. The exploration of transferability in these models requires further studies that may involve conditional text variables, noisy images, and various other non-trivial aspects.

Q5: A visualization of all the edit directions discovered via SVD would be quite interesting. Are they all semantically meaningful?

A5: Thanks for proposing the interesting question. We have attached the identified editing directions for different regions of interest in Figure C of the global response PDF. These editing directions are selected from CelebA, FFHQ, and AFHQ.

1. We observe that the editing directions demonstrate semantics correspondences to the region of interest. We also notice for these datasets, the position of objects is biased in the center of images, which benefits the transferability of editing directions.
2. However, from our observation, the transferability is robust to gender difference, facial feature shape difference, and moderate position difference, as presented in Figure 1(b) of the main paper and Figure B of the global response PDF.

Thank you for all the valuable suggestions and for recognizing the value of our work! We will expand the discussion on global editing and transferability in conditional diffusion models and will discuss BoundaryDiffusion in the paper. We have carefully read through BoundaryDiffusion, which is an interesting supervised one-step global edit method. BoundaryDiffusion uses linear SVMs to classify image latent by hyperplanes using label annotations, and about 100 images are required for each class. The edit intuitively moves the image latent in both $\epsilon_t$ and $h_t$ spaces to the negative or positive side of the hyperplane, so that the corresponding semantic is reduced or enhanced. Although the linear and one-step edit properties are similar, our method is (a) localized, (b) requires no label annotation, (c) can find transferable directions using a single image, (d) requires edits only in $x_t$ space, and (e) has a theoretical basis to support the approach. Thanks for the constructive feedback, we will make sure all of them are reflected in our final manuscript.

We thank the reviewer for constructive feedback. During rebuttal, we address the reviewer’s concerns on the experiments and other questions as follows.

Q1. Limited experimental evidence and quantitative and qualitative comparisons.

A1: Thanks to the reviewer's suggestions, we added more results, and conducted more qualitative and quantitative comparisons with more baselines to better evaluate our method. We refer detailed results and discussion to Q&A 1 of the global response.

Q2. Detailed ablation study on sensitivity to various parameters...

A2: Thanks to the reviewer's suggestions, we conducted more detailed ablation studies and gave a more comprehensive summary. We refer detailed results and discussion to Q&A 2 of the global response.

Q3: Validation of using the low-rank Gaussian distributions.

A3: In [1], the authors conducted extensive empirical experiments and found that for diffusion models trained on the FFHQ and AFHQ datasets, the learned score can be approximated by the linear score of a Gaussian, particularly at high noise levels. Furthermore, [2] confirms the low-dimensional nature of various image datasets, such as CIFAR-10 and ImageNet, and calculates their intrinsic dimensions. Building on these findings, we incorporate the concept of Gaussian distribution and low-dimensional properties to study the low-rank Gaussian case. This approach enables our model to effectively capture the core structure of image data while remaining tractable for theoretical analysis, thus serving as a practical foundation for theoretical studies on real-world image datasets.

We will integrate these discussions into the final version to enhance motivation.

Q4. Clarification on Posterior Mean Predictor (PMP).

A4:

1. Definition & computation of PMP and reference for it’s derivation: Indeed, PMP is a network function in diffusion models, which takes an input pair ($x_t$, $t$), and outputs the predicted posterior mean $\hat{x}\_{0,t}$. Specifically, the computation of PMP in diffusion models is defined in Equation (2), where $\epsilon_{\theta}$ is the learned unet denoiser in the diffusion model. We refer how PMP is derived to the derivation of Equation (12) in the DDIM paper [3].
2. How local linearity and low-rankness in PMP is utilized: (1) PMP’s local linearity is the key assumption for finding edit direction via SVD of PMP’s Jacobian, since directions found via SVD are meaningful only if PMP is linear; (2) PMP’s local linearity also leads to the linear and composable properties of the LOCO edit method; (3) PMP’s low-rankness ensures us to use a low-rank estimation to find the nullspace, achieving efficient and effective nullspace projection.

We will make the above points clear in the final version.

Q5: Clarification on finding the precise and disentangled edit direction.

• Elaborate on what $P_{\Omega}$... using masking techniques.
• Explain how performing the Jacobian... helps... for precise local editing

A5: We would like to clarify concepts, process, and intuition in finding such local edit direction. We will also revise the writing to make the points clearer.

1. Definition of ROI, $P_{\Omega}$ and $P_{\Omega^C}$: Here, $\Omega$ is an index set that covers the region of interest (ROI) and $\Omega^C$ covers any other region in the image outside ROI. Based upon this, $P_{\Omega}$ and $P_{\Omega^C}$ denote the projections onto $\Omega$ and $\Omega^C$, respectively. Intuitively speaking, $P_{\Omega}(I)$ crops the content of an image $I$ within the mask, and $P_{\Omega^C}(I)$ crops the contents of $I$ outside of the mask.
2. Decomposition of $\hat{x}\_{0,t}$ and calculation of Jacobians: Based on the above definition, we decompose PMP’s output $\hat{x}\_{0,t}$ into $\tilde{x}\_{0,t}$ and $\bar{x}\_{0,t}$ as visualized in Figure 3, where $\tilde{x}\_{0,t} = P_{\Omega}(\hat{x}\_{0,t})$ and $\bar{x}\_{0,t} = P_{\Omega^C}(\hat{x}\_{0,t})$. We further define $\tilde{J}\_{\theta,t} = \partial \tilde{x}\_{0,t} /\partial x_t$ and $\bar{J}\_{\theta,t} = \partial \bar{x}\_{0,t} /\partial x_t$.
3. Finding image editing directions and nullspace via SVD of Jacobians: Let $\tilde{J}\_{\theta,t} = \tilde{U}\tilde{S}\tilde{V}^T$, and $\bar{J}\_{\theta,t} = \bar{U}\bar{S}\bar{V}^T$ be the compact SVD. Intuitively, $span(\tilde{V}) = range(\tilde{J}\_{\theta,t}^T)$ is the subspace containing change directions of $x_t$ that leads to change within the $\tilde{x}\_{0,t}$. Besides, $span(\bar{V}) = range(\bar{J}\_{\theta,t}^T)$ is the subspace containing change directions of $x_t$ that leads to edit in $\bar{x}\_{0,t}$. Moreover, $nullspace(\bar{J}\_{\theta,t})$ is the subspace leads to no edit in $\bar{x}\_{0,t}$.
4. Nullspace projection for more precise and disentangled image editing: For a direction $v \in range(\tilde{J}\_{\theta,t}^T)$, nullspace projection means projecting $v$ onto $nullspace(\bar{J}\_{\theta,t})$. In practice, this nullspace projection can be calculated as $v_p = (I - \bar{V}\bar{V}^T) v$. Such nullspace projection can further eliminate the effect of $v_p$ to change within $\bar{x}\_{0,t}$, and disentangle the change to be only within $\tilde{x}\_{0,t}$. Then by denoising $x_t + \lambda v_p$, the new image is more precisely edited within the ROI $\Omega$.

[1] Binxu et al., "The Hidden Linear Structure in Score-Based Models and its Application." 2023.

[2] Phillip et al., "The intrinsic dimension of images and its impact on learning." ICLR 2021.

[3] Jiaming et al., Denoising diffusion implicit models. 2020.

Thanks for the questions, we would like to further make clarifications on these points.

1. We have extended the comparisons with two additional baselines BlendedDiffusion [2] and NoiseCLR [1] for comparison. See global rebuttal Q&A 1 and pdf Tab. A and Fig. E.

2. (1) The human evaluation dataset is randomly selected have high diversity to cover various semantic directions; (2) Asyrp [3] uses only 40 data samples for human evaluation on CelebA (Appendix K.1), Pullback [4] only shows qualitative results; (3) BlendedDiffusion and NoiseCLR do not mention the size of evaluation dataset; (4) A further detail is, we used 400 samples for other added metrics LPIPS and SSIM. Hence, we think the evaluation dataset size is robust enough to provide fair comparisons.

3. The mentioned FID and IS are good metrics measuring whether generated image distributions are similar to the training images, but not standard metrics for image editing methods. (1) FID and IS will be increased if additional features are edited in comparison to the original one; (2) Representative baslines including NoiseCLR, BlendedDiffusion, Asyrp, and Pullback use neither of the FID and IS; (3) As in global rebuttal Q&A 1 and pdf Tab. A, we have conducted a comprehensive comparison using 7 metrics and 4 attributes to show the superiority of our method. This indeed supports that we have conducted comprehensive empirical evidence in addition to the solid theoretical basis which is lacking in the previous papers.

4. For more ablation studies, as summarized in Q2&A2 for the global response, we do more ablation studies on Noise levels (i.e., time steps), Perturbation strength, Nullspace projection, and ranks. We have shown representative examples, and more results will be included in the revision.

We appreciate the reviewers' prompt responses and make further clarification and references on how we conduct comprehensive experiments to show the superiority of our method. We kindly request the reviewer evaluate our work fairly based on the rebuttal and our further clarifications.

[1] Yusuf et al., Noiseclr: A contrastive learning approach for unsupervised discovery of interpretable directions in diffusion models. CVPR 2024.

[2] Omri et al., Blended diffusion for text-driven editing of natural images. CVPR 2022.

[3] Mingi et al. Diffusion models already have a semantic latent space. ICLR 2023.

[4] Yong et al. Understanding the latent space of diffusion models through the lens of riemannian geometry. NeurIPS 2023.

We thank the reviewer’s constructive feedback, and in the following we address the reviewer’s concerns one-by-one.

Q1: Not enough qualitative and quantitative results and comparisons with existing work.

Thanks to the reviewer's suggestions, we conduct more qualitative and quantitative comparisons with more baselines, and add more results to better evaluate our method. We refer detailed results and discussion to Q&A 1 of the global response.

Q2. Not convincing empirical results.

1. Fig. 6 is not convincing to show better localized editing with LOCO than Asyrp
2. Why Transfer CLIP Score of Asyrp is better than LOCO, and whether it’s an issue

A2: We thank the reviewer for raising these constructive points which improve our work.

1. More convincing visualizations.
   • To demonstrate the effectiveness of our method, we selected examples in Fig. 6 where Asyrp achieves its best performance, yet our method still performs even better. For instance, in Fig. 6, to edit lips, Asyrp noticeably alters undesired regions such as face color, hair shape, and face shape more than our method.
   • There are many other instances where Asyrp's editing changes the image much more significantly than ours. We add more random examples in Figure E of the global PDF to visualize the local edit ability of our method in comparison of others.
2. Discussion on the Transfer CLIP Score in Table 1. Very good question for a deeper discussion.
   • The higher transfer CLIP score of Asyrp is because it is directly supervised by the CLIP score to learn each concept and predict editing directions. In contrast, our method is unsupervised and learning-free, and has the best CLIP score among other unsupervised methods.
   • Moreover, the transfer CLIP score is biased by large changes in Asyrp: For successful edit in both Asyrp and LOCO, Asyrp tends to have larger global changes resulting in a much higher transfer CLIP score, sometimes leading to corruption in other parts though the desired region is edited. Examples are shown in Figure E of the global PDF.
   • Additionally, the transfer CLIP score relies on CLIP's intrinsic failures to capture detailed semantics as discovered in [1], which may lead to edit failures of Asyrp. Failure examples that are potentially related are shown in Figure E (row 5-8) of the global PDF, where Asyrp fails to edit darker eyebrows for all random examples.
   • Therefore, to compensate for the biases of the transfer CLIP score, we also measure the local edit success rate, where our method outperformed all others. Thanks to the reviewer for raising the point, we also add LPIPS [2] and SSIM [3] as guardians of dramatic changes and use the less biased local edit success rate as the major evaluation metric for local edit ability.

In the revision, we will include those discussions in the paper to clarify our findings.

Q3: The provided theoretical framework concerns mainly the undirected image editing part; how text-directed image editing behaves is not addressed by the proposed method. This is a certain limitation, that weakens the generality of the proposed method, yet it doesn't reduce the importance of the theoretical results provided.

A3: We thank the reviewer for raising the points, but we want to clarify this further.

1. In Figure 4, we showed that our method can be extended to text-directed image editing. This demonstrates the generality of our edit approach.
2. Second, the empirical observation of low-rankness and local linearity is generalizable to text-to-image diffusion models as shown in Figure 2 and Figure 9.
3. Although our theoretical study part is for unconditional diffusion models, to the best of our knowledge, our work is the first theoretically ground method compared to all previous diffusion model based editing methods. It's an advantage compared to other image edit methods.
4. Besides, for studying text-directed diffusion models, the challenges lie in the more complicated feature space caused by a mixture of image and text distributions. Understanding their feature space is yet an unsolved problem in the area. Hope our work can provide some inspiration for future exploration.

[1] Shengbang et al., Eyes wide shut? exploring the visual shortcomings of multimodal llms. CVPR 2024

[2] Richard et al. The unreasonable effectiveness of deep features as a perceptual metric. CVPR 2018.

[3] Zhou et al., Image Quality Assessment: From Error Visibility to Structural Similarity. 2004

We thank the reviewer’s constructive feedback, and in the following we address the reviewer’s concerns one-by-one.

Q1: The computation time of the method is still a bit long (taking around 70s if I understand correctly)

A1:

1. Compared with the global edit method Pullback [25], the additional cost is introduced from finding local edit direction, yet the addition cost is not significant.
2. Besides, we add additional comparisons with a local edit method BlendedDiffusion [1] in Table A of the global response PDF, where our method is more efficient in learning time.
3. Moreover, our method can transfer the local edit direction to other images with a high successful rate and no additional time cost in learning. On the contrary, other local/global edit methods cannot transfer the edit direction (BlendedDiffusion) or have weaker transferability as summarized in Table A.

Q2: Whether the homogeneity of the editing can be observed on samples that are very different: e.g.,

• computing editing direction on an image with a face at the left, and transfer to an image with a face on the right;
• computing editing direction on an image with realistic style, and transfer to an image with cartoon style.

A2: This is a good question. We present more results and extend the discussions.

1. • For unconditional diffusion models on FFHQ and CelebA, we can transfer edit directions to faces on the different side, as presented in Figure B of the global response PDF. But we do notice that these datasets tend to have the object in the center, which benefits the transferability.
   • We have further attached the visualization of editing directions in Figure C, and the edit direction has semantic correspondences to the target edit region. From our observation, the transferability is robust to gender differences, facial feature shape differences, and moderate position differences in FFHQ and CelebA.
2. • To achieve goal (2), conditional diffusion models are required. We have previously explored such transferability in stable diffusion models, and the transfer success rate is low. By our analysis, the homogeneity needs the images lie in the same subspace, but the manifold of images with different styles in conditional diffusion models may violate this.
   • Understanding the feature space of conditional diffusion models is a challenging and unsolved problem in the area, since the feature space is related to text prompts and noisy images. We are interested in exploring the question, and hope our theoretical analysis in unconditional diffusion models can provide some inspiration for future works.

Q3: In addition, since current models such as SD3 are using the flow-matching objective to train the model, I wonder if such observed phenomenon would be more prominent on these models?

A3:

1. This is an interesting question and we have explored it further. Due to time constraints, we study the low-rankness and local linearity of SiT [2], a simpler diffusion model using the flow-matching objective at training. As presented in Figure F of the global response PDF, we do see generalized local linearity, and a similar low-rank trend in SiT, though the rank is not exactly as low as other diffusion models. It would be interesting to study the differences in low-rank subspace between diffusion models trained under different objectives, and test other diffusion models trained using flow-matching objectives such as Stable Diffusion 3.

[1] Omri et al., Blended diffusion for text-driven editing of natural images. CVPR 2022.

[2] Nanye et al., "Sit: Exploring flow and diffusion-based generative models with scalable interpolant transformers." 2024.