SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$$
\begin{array}{l} \mathcal {L} _ {x \rightarrow y \rightarrow x} = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} | | x _ {0} - G (y _ {t}, c _ {x}, x _ {0}) | | _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} | | x _ {0} - \left[ y _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {\theta} (y _ {t}, c _ {x}, x _ {0}) \right] / \sqrt {\bar {\alpha} _ {t}} | | _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} | | x _ {0} - \left[ \sqrt {\bar {\alpha} _ {t}} \bar {y} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {y} - \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {\theta} (y _ {t}, c _ {x}, x _ {0}) \right] / \sqrt {\bar {\alpha} _ {t}} | | _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} \left| \left| x _ {0} - \bar {y} _ {0} + \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} \left[ \varepsilon_ {\theta} \left(y _ {t}, c _ {x}, x _ {0}\right) - \varepsilon_ {y} \right] \right| \right| _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} \left| \left| x _ {0} - G (x _ {t}, c _ {y}, x _ {0}) + \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} \left[ \varepsilon_ {\theta} (y _ {t}, c _ {x}, x _ {0}) - \varepsilon_ {y} \right] \right| \right| _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} \left| \left| x _ {0} - x _ {t} / \sqrt {\bar {\alpha} _ {t}} + \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} \left[ \varepsilon_ {\theta} \left(x _ {t}, c _ {y}, x _ {0}\right) + \varepsilon_ {\theta} \left(y _ {t}, c _ {x}, x _ {0}\right) - \varepsilon_ {y} \right] \right| \right| _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} \left| \left| x _ {0} - (\sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {x}) / \sqrt {\bar {\alpha} _ {t}} + \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} [ \varepsilon_ {\theta} (x _ {t}, c _ {y}, x _ {0}) + \varepsilon_ {\theta} (y _ {t}, c _ {x}, x _ {0}) - \varepsilon_ {y} ] \right| \right| _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} \left| \left| \varkappa \sigma - \varkappa \sigma + \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} \left[ \varepsilon_ {\theta} \left(y _ {t}, c _ {x}, x _ {0}\right) + \varepsilon_ {\theta} \left(x _ {t}, c _ {y}, x _ {0}\right) - \varepsilon_ {x} - \varepsilon_ {y} \right] \right| \right| _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}, \varepsilon_ {y}} \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} | | \varepsilon_ {\theta} (y _ {t}, c _ {x}, x _ {0}) + \varepsilon_ {\theta} (x _ {t}, c _ {y}, x _ {0}) - \varepsilon_ {x} - \varepsilon_ {y} | | _ {2} ^ {2} \\ \end{array}
$$
Invariance Loss Dropping the variances,  $\mathcal{L}_{x\to y\to y} = \mathbb{E}_{x_0,\varepsilon_x}||\varepsilon_\theta (x_t,c_y,x_0) - \varepsilon_\theta (x_t,c_y,\bar{y}_0)||_2^2.$
$$
\begin{array}{l} \mathcal {L} _ {x \rightarrow y \rightarrow y} = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} | | \bar {y} _ {0} - G (x _ {t}, c _ {y}, \bar {y} _ {0}) | | _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} | | G (x _ {t}, c _ {y}, x _ {0}) - G (x _ {t}, c _ {y}, \bar {y} _ {0}) | | _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} | | \left[ \mathcal {Y} - \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {\theta} \left(x _ {t}, c _ {y}, x _ {0}\right) \right] / \sqrt {\bar {\alpha} _ {t}} - \left[ \mathcal {Y} - \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {\theta} \left(x _ {t}, c _ {y}, \bar {y} _ {0}\right) \right] / \sqrt {\bar {\alpha} _ {t}} | | _ {2} ^ {2} \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} | | \varepsilon_ {\theta} (x _ {t}, c _ {y}, x _ {0}) - \varepsilon_ {\theta} (x _ {t}, c _ {y}, \bar {y} _ {0}) | | _ {2} ^ {2} \\ \end{array}
$$
A.3 Proof of Self Regularization
Let  $\varepsilon_{\theta}^{*}$  denote the denoising autoencoder of the pre-trained text-guided LDM backbone with a generation function  $G^{*}$ . Note that  $x_{t} = S(x_{0},\varepsilon_{x})$
$$
\begin{array}{l} \mathcal {L} _ {\mathrm {L D M}} = 1 - \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} P [ G (x _ {t}, c _ {y}, x _ {0}), c _ {y} ] - 1 \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} \left| 1 - P \left[ G \left(x _ {t}, c _ {y}, x _ {0}\right), c _ {y} \right] \right| - 1 \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} \left| 1 - P \left[ G ^ {*} \left(x _ {t}, c _ {y}\right), c _ {y} \right] + P \left[ G ^ {*} \left(x _ {t}, c _ {y}\right), c _ {y} \right] - P \left[ G \left(x _ {t}, c _ {y}, x _ {0}\right), c _ {y} \right] \right| - 1 \\ \leq \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} \left| 1 - P \left[ G ^ {*} \left(x _ {t}, c _ {y}\right), c _ {y} \right] \right| + \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} \left| P \left[ G ^ {*} \left(x _ {t}, c _ {y}\right), c _ {y} \right] - P \left[ G \left(x _ {t}, c _ {y}, x _ {0}\right), c _ {y} \right] \right| - 1 \\ \end{array}
$$
Note that  $\mathbb{E}_{x_0,\varepsilon_x}\left|1 - P\big[G^* (x_t,c_y),c_y\big]\right| := \mathbb{E}_{\mathrm{LDM}}^*$  is the translation error likelihood of the pre-trained LDM backbone. According to the domain smoothness in Assumption 1, we have:
$$
\begin{array}{l} \mathcal {L} _ {\mathrm {L D M}} \leq \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} \left| P \left[ G ^ {*} (x _ {t}, c _ {y}), c _ {y} \right] - P \left[ G (x _ {t}, c _ {y}, x _ {0}), c _ {y} \right] \right| + \mathbb {E} _ {\mathrm {L D M}} ^ {*} - 1 \\ \leq \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} L \left| \left| G ^ {*} (x _ {t}, c _ {y}) - G (x _ {t}, c _ {y}, x _ {0}) \right| \right| + \mathbb {E} _ {\mathrm {L D M}} ^ {*} - 1 \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} L \left| \left| \left[ \mathcal {Y} - \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {\theta} ^ {*} (x _ {t}, c _ {y}) \right] / \sqrt {\bar {\alpha} _ {t}} - \left[ \mathcal {Y} - \sqrt {1 - \bar {\alpha} _ {t}} \varepsilon_ {\theta} (x _ {t}, c _ {y}, \bar {y} _ {0}) \right] / \sqrt {\bar {\alpha} _ {t}} \right| \right| + \mathbb {E} _ {\mathrm {L D M}} ^ {*} - 1 \\ = \mathbb {E} _ {x _ {0}, \varepsilon_ {x}} L \sqrt {\frac {1 - \bar {\alpha} _ {t}}{\bar {\alpha} _ {t}}} | | \varepsilon_ {\theta} (x _ {t}, c _ {y}, x _ {0}) - \varepsilon_ {\theta} ^ {*} (x _ {t}, c _ {y}) | | _ {2} + \mathbb {E} _ {\mathrm {L D M}} ^ {*} - 1 \\ \end{array}
$$
B Scientific Artifacts and Licenses
B.1 The ManiCups Dataset
We introduce ManiCups, a dataset that tasks image editing models to manipulate cups by filling or emptying liquid to/from containers, curated from human-annotated bounding boxes in publicly available datasets and Bing Image Search (under Share license for training and Modify for test set). The dataset consists of a total of 5714 images of empty cups and cups of coffee, juice, milk, and water. We describe our three-stage data collection pipeline in the following paragraphs.
In the Image Collection stage, we gather raw images of interest from MSCOCO [26], Open Images [23], as well as Bing Image Search API. For the MSCOCO 2017 dataset, we specifically searched for images containing at least one object from the categories of "bottle," "cup," and "wine glass." Regarding the Open Images v7 dataset, our search focused on images with at least one object falling under the categories of "coffee," "coffee cup," "mug," "juice," "milk," and "wine glass." To conduct the Bing Image Search, we utilized API v7 and employed queries with the formats "empty <container>" and "<container> of <liquid)." The <container> category encompasses cups, glasses, and mugs, while the <liquid> category includes coffee, juice, water, and milk. We obtained approximately 30,000 image candidates after this step.
During the Image Extraction stage, we extract regions of interest from the candidate images and resize them to a standardized size of  $512 \times 512$  pixels. Specifically, for subsets obtained from MSCOCO and Open Images, we extract the bounding boxes with labels of interest. To ensure a comprehensive representation, each bounding box is extended by  $5\%$  on each side, and the width is adjusted to create a square window. In cases where the square window exceeds the image boundaries, we shift the window inwards. If, due to resizing or shifting, a square window cannot fit within the image, we utilize the cv2.BORDER_REPLICATE function to replicate the edge pixels. All bounding boxes with an initial size less than  $128 \times 128$  are discarded, and the remaining images are resized to a standardized size of  $512 \times 512$  pixels. The same approach is applied to images obtained from the Bing Search API, utilizing cv2.BORDER_REPLICATE for edge pixel replication. Following this step, we obtained approximately 20,000 extracted and resized images.
In the Filtering and Labeling stage, our focus is on controlling the quality of images and assigning appropriate labels. Our filtering process begins by identifying and excluding replicated images using the L2 distance metric. Subsequently, we leverage the power of CLIP to detect and remove images containing human faces, as well as cups with a front-facing perspective. Additionally, we use CLIP to classify the remaining images into their respective domains. To ensure the accuracy of the dataset, three human annotators thoroughly review the collected images, verifying that the images portray a top-down view of a container and assigning the appropriate labels to the respective domains. The resulting ManiCups dataset contains 5 domains, including 3 abundant domains (empty, coffee, juice) with more than 1K images in each category and 2 low-resource domains (water, milk) with less than 1K images to facilitate research and analysis in data-efficient learning.
To our knowledge, ManiCups is one of the first datasets targeted to the physical state changes of objects, other than stylistic transfers or type changes of objects. The ability to generate consistent state changes based on manipulation is fundamental for future coherent video prediction [14] as well as understanding and planning for physical agents [49?]. We believe that ManiCups is a valuable resource to the community.
B.2 Dataset Statistics
We present the statistics of the ManiCups in Table 3, and other scene/object level datasets in Table 4.
Domains	Train	Test	Total
Empty Cup	1256	160	1416
Cup of Coffee	1550	100	1650
Cup of Juice	1754	100	1854
Cup of Water	801	50	851
Cup of Milk	353	50	403
Total	5714	460	6174
Table 3: The statistics of the ManiCups dataset, with 3 abundant domains and 2 lowresource domains.
Domains	Train	Test	Total
Summer	1231	309	1540
Winter	962	238	1200
Horse	1067	118	1194
Zebra	1334	140	1474
Apple	995	256	1251
Orange	1019	248	1267
B.3 Licenses of Scientific Artifacts
We present a complete list of references and licenses in Table 5 for all the scientific artifacts we used in this work, including data processing tools, datasets, software source code, and pre-trained weights.
Table 4: The statistics of the Yosemite summer  $\leftrightarrow$  winter, horse  $\leftrightarrow$  zebra, and apple  $\leftrightarrow$  orange datasets.
Data Sources	URL	License
FiftyOne (Tool)	Link	Apache v2.0
Summer2Winter Yosemite	Link	ImageNet, See Link
Horse2Zebra	Link	ImageNet, See Link
Apple2Orange	Link	ImageNet, See Link
MSCOCO 2017	Link	CC BY 4.0
Open Images v7	Link	Apache v2.0
Bing Image Search API v7	Link	Share (training) & Modify (test)
Software Code	URL	License
Stable Diffusion v1	Link	CreativeML Open RAIL-M
Stable Diffusion v2	Link	CreativeML Open RAIL++-M
ControlNet	Link	Apache v2.0
CUT	Link	Mixed, See Link
Prompt2Prompt + NullText	Link	Apache v2.0
Stable Diffusion Inpainting	Link	MIT license
Text2LIVE	Link	MIT license
Stable Diffusion SDEdit	Link	Apache v2.0
Cycle diffusion	Link	Apache v2.0
ILVR	Link	MIT license
EGSDE	Link	N/A
P2-weighting	Link	MIT license
Pix2pix-zero	Link	MIT license
Masactrl	Link	Apache v2.0
Metric Implementations	URL	License
FID	Link	Apache v2.0
FCD	Link	MIT license
CLIP Score	Link	Apache v2.0
PSNR & SSIM	Link	BSD-3-Clause
L2 Distance	Link	BSD-3-Clause
Table 5: License information for the scientific artifacts used.
C.1 Computational Resources
Table 6 illustrates the training performance of CycleNet and FastCycleNet on a single NVIDIA A40 GPU under  $256 \times 256$  with batch size of 4. The table provides information on the training speed in seconds per iteration and the memory usage in gigabytes for both models. FastCycleNet exhibits a faster training speed of 1.1 seconds per iteration while consuming 24.5 GB of memory. On the other hand, CycleNet demonstrates a slightly slower training speed of 1.8 seconds per iteration, and it requires 27.9 GB of memory.
Training	Train Speed (sec/iteration)	Mem Use (GB)
FastCycleNet	1.1	24.5
CycleNet	1.8	27.9
Table 6: Speed of CycleNet and FastCycleNet
C.2 Hyper-parameter Decisions
We include the major hyper-parameter tuning decisions for reproducibility purposes. In the training of CycleNet, the weights of our three loss functions are respectively set as  $\lambda_1 = 1$ ,  $\lambda_2 = 0.1$ , and  $\lambda_3 = 0.01$ . We train the model for 50k steps. Following [29], we initialize the sampling process with the latent noised input image  $z_{t}$ , collected using Equation 1. A standard 50-step sampling is applied at inference time with  $t = 100$ . Our configuration is as follows:
model:  
params:  
    linear_start: 0.00085  
    linear_end: 0.0120  
    num_timesteps_cond: 1  
    timesteps: 1000  
    image_size: 64  
    channels: 4  
    cond階段_trainable: false  
    monitor: val/loss.simple_ema  
    scale_factor: 0.18215  
    use_ema: False  
    only_mid_control: False  
    recon_weight: 1 # lambda1  
    disc_weight: 0.1 # lambda2  
    cycle_weight: 0.01 # lambda3  
    disc_mode: eps  
    consis_weight: 0.1
For more details, please refer to the supplementary codes.
C.3 Baseline Implementations
- CycleGAN: We used some of the results provided in [34].
- CUT: We used the official code<sup>4</sup> provided by the authors.
- Inpainting + ClipSeg: we modified from the gradio<sup>5</sup> provided by the community.
- Text2LIVE: We used the official code provided by the authors.
- ILVR: We first pre-train the diffusion model using P2-weighting [6], and then generated output using the official code<sup>7</sup> provided by the authors.
<sup>4</sup>https://github.com/taesungp/contrastive-unpaired-translation
<sup>5</sup>https://huggingface.co/spaces/multimodalart/stable-diffusion-inpainting
<https://github.com/omerbt/Text2LIVE
<sup>7</sup>https://github.com/jychoi118/ilvr_adm
- EGSDE: We first pre-train the diffusion model using P2-weighting [6], and then generated output using the official code<sup>8</sup> provided by the authors.
- SDEdit: We used the community implementation<sup>9</sup> of SDEdit based on stable diffusion.
- CycleDiffusion: We modified from the official gradio<sup>10</sup> provided by the authors.
- Prompt2Prompt + NullText: We used the official code<sup>11</sup> provided by the authors.
- Masactrl: We used the official code  ${}^{12}$  provided by the authors.
- Pix2pix-zero: We used the official code<sup>13</sup> provided by the authors, and we generated the summer2winter direction assets following the scripts provided by the authors.
C.4 Evaluation Metrics Explained
Image Quality To evaluate the quality of images, we employ two metrics.
- Fréchet Inception Distance (FID) [12] is a widely used metric in image generation tasks. A lower FID score indicates better image quality and more realistic samples.
-  $\mathbf{FID}_{\mathrm{clip}}$  [24] combines the FID metric with features extracted with a CLIP [36] encoder, providing better assessment of image quality. Similar to FID, a lower  $\mathbf{FID}_{\mathrm{clip}}$  score represents better image quality.
Translation Quality To measure to what extent is the translation successful, we use the CLIP Score [11], i.e., the CLIP model [36] to obtain the latent representations of images and prompts, and then calculate the cosine similarity between them. A higher CLIP score indicates a stronger similarity between the generated image and the text prompt, thus better translation.
Translation Consistency We measure translation consistency using four different metrics.
- L2 Distance is a measure of the Euclidean distance between two images. A lower L2 distance indicates higher similarity and better translation consistency.
- Peak Signal-to-Noise Ratio (PSNR) [4] measures the ratio between the maximum possible power of a signal and the power of corrupting noise. A higher PSNR score indicates better translation consistency.
- Structural Similarity Index Measure (SSIM) [47] is a metric used to compare the structural similarity between two images. A higher SSIM score suggests higher similarity and better translation consistency.
- Learned Perceptual Image Patch Similarity (LPIPS) [52] is a comprehensive evaluation metric for the perceptual similarity between two images. A lower LPIPS score indicates higher perceptual similarity.
While CycleNet holds great promise, it is essential to address potential broader impacts, including ethical, legal, and societal considerations. One significant concern is copyright infringement. As an image translation model, CycleNet can potentially be used to create derived works from artists' original images, raising the potential for copyright violations. To safeguard the rights of content creators and uphold the integrity of the creative economy, it is imperative to prioritize careful measures and diligently adhere to licensing requirements. Another critical aspect to consider is the potential for fabricated images to contribute to deception and security threats. If misused or accessed by malicious actors, the ability to generate realistic fake images could facilitate misinformation campaigns, fraud, and even identity theft. This underscores the need for responsible deployment and robust security measures to mitigate such risks. CycleNet leverages pre-trained latent diffusion models, which may encode biases that lead to fairness issues. It is worth noting that the proposed method is currently
<sup>8</sup>https://github.com/ML-GSAI/EGSDE
<sup>9</sup>https://huggingface.co/docs/diffusers
<sup>10</sup>https://huggingface.co/spaces/ChenWu98/Stable-CycleDiffusion
11https://github.com/google/prompt-to-prompt
12https://github.com/TencentARC/MasaCtrl
<sup>13</sup>https://github.com/pix2pixzero/pix2pix-zero
purely algorithmic, devoid of pre-training on web-scale datasets itself. By acknowledging and actively addressing these broader impacts, we can work towards harnessing the potential of CycleNet while prioritizing ethics, legality, and societal well-being.
E Addendum to Results
E.1 Choice of Pre-trained LDM Backbone
For all experiments in the main paper, we use Stable Diffusion  $2.1^{14}$  as the pre-trained LDM backbone. We additionally attach a quantitative comparison of CycleNet using Stable Diffusion  $1.5,^{15}$  which indicates marginal differences in practice.
Tasks	summer→winter (512 × 512)	horse→zebra (512 × 512)
Metrics	FID↓	FIDclip↓	CLIP↑	LPIPS↓	PSNR↑	SSIM↑	L2×106↓	FID↓	FIDclip↓	CLIP↑	LPIPS↓	PSNR↑	SSIM↑	L2×106↓
SD v1.5	83.45	15.21	23.56	0.17	25.40	0.74	1.39	73.34	25.42	27.77	0.25	20.96	0.64	0.79
SD v2.1	79.79	15.39	24.12	0.15	25.88	0.69	1.23	76.83	24.78	25.27	0.08	26.21	0.74	0.59
E.2 Image Resolution
We notice that the Stable Diffusion [38] backbone is pre-trained in multiple stages, initially at a resolution of  $256 \times 256$  and followed by another stage at a resolution of  $512 \times 512$  or beyond. This could potentially lead to the under-performance of zero-shot diffusion-based methods on summer→winter and horse→zebra, which are at a resolution of  $256 \times 256$ . We repeat the experiment on these two tasks at a generation resolution of  $512 \times 512$  and report the results in Table 8. It's important to acknowledge that this particular setting presents an unfair comparison with considerable challenges for our methods, primarily because the training images are set at a resolution of  $256 \times 256$ , yet our model is expected to adapt to a higher resolution. Still, we observe a competitive performance of our models, especially in summer→winter. The diminished effectiveness of our method in the horse→zebra task can be attributed to the fact that the zebra patterns, initially acquired at a resolution of  $256 \times 256$ , lose realism and become overly dense when scaled up to  $512 \times 512$  (see Example 3, Figure 11). This limitation can potentially be addressed by scaling to images with multiple resolutions.
Table 7: A quantitative comparison using Stable Diffusion 1.5 and 2.1.
Tasks	summer→winter (Global, 512 × 512)	horse→zebra (Local, 512 × 512)
Metrics	FID↓	FIDclip↓	CLIP ↑	LPIPS↓	PSNR↑	SSIM↑	L2×104↓	FID↓	FIDclip↓	CLIP ↑	LPIPS↓	PSNR↑	SSIM↑	L2×104↓
Mask-based Diffusion Methods
Inpaint + ClipSeg	168.43	46.48	26.57	0.65	9.01	0.13	4.07	79.14	26.05	28.71	0.29	16.89	0.60	1.95
Text2LIVE	86.12	18.30	25.98	0.27	16.83	0.68	1.67	103.14	22.71	31.55	0.16	20.98	0.81	2.08
Mask-free Diffusion Methods
ControlNet + Canny	179.17	44.71	25.01	0.61	9.97	0.19	7.23	112.63	68.31	27.22	0.6	8.52	0.06	8.65
ILVR	101.26	27.72	21.71	0.58	9.87	0.18	3.70	194.92	45.44	23.90	056	10.06	0.24	7.27
EGSDE	108.71	35.89	21.80	0.37	19.84	0.39	2.40	161.26	39.94	25.52	0.36	20.67	0.40	2.15
SDFEdit	90.51	21.23	23.26	0.30	18.59	0.43	1.39	63.04	22.65	27.97	0.33	18.49	0.44	2.96
Pix2Pix-Zero	88.79	83.78	23.63	0.29	20.91	0.62	2.15	115.52	29.74	27.42	0.37	18.18	0.57	3.14
MasaCtrl	114.83	29.18	17.11	0.37	14.66	0.43	2.28	239.61	47.48	21.15	0.41	16.31	0.37	1.83
P2P + NullText	92.65	22.46	24.82	0.24	20.19	0.66	1.15	106.83	26.49	26.57	0.21	21.45	0.66	2.04
CycleDiffusion	84.52	20.85	24.40	0.24	21.66	0.68	0.98	41.17	18.10	29.09	0.29	19.41	0.61	2.53
FastCycleNet	78.43	14.99	24.33	0.16	25.81	0.76	1.24	72.68	25.34	24.42	0.13	26.74	0.72	1.12
CycleNet	79.79	15.39	24.12	0.15	25.88	0.69	1.23	76.83	24.78	25.27	0.08	26.21	0.74	0.59
Table 8: A quantitative comparison of various image translation models for the summer→winter and horse→zebra at  $512 \times 512$ .
E.3 Sudden Convergence
As shown in Figure 8, CycleNet can translate an input image of summer to winter at the beginning of training with no consistency observed. Similar to ControlNet [51], CycleNet also demonstrates the sudden convergence phenomenon, which usually happens around  $3\mathrm{k}$  to  $8\mathrm{k}$  iterations of training.
E.4 Additional Quantitative Results
In Table 9, we present the complete numerical performance of the state-changing tasks on ManiCups. In general, we found that emptying a cup is a more challenging image editing task for most of
$^{14}$ https://huggingface.co/stabilityai/stable-diffusion-2-1
15https://huggingface.co/runwayml/stable-diffusion-v1-5
Figure 8: Sudden convergence appears at around  $3\mathrm{k}$  -  $8\mathrm{k}$  in our experiments.
the existing computation models, compared to filling a cup with liquid. CycleNet shows superior performance, especially in domains with abundant training samples (coffee and juice). We also observe that the performance is marginally less competitive in low-resource domains (milk and water). We leave it to future work to explore more data-efficient models that fine-tune pre-trained latent diffusion models with cycle consistency granted.