The Crystal Ball Hypothesis in diffusion models: Anticipating object positions from initial noise

## Abstract

Abstract Diffusion models have achieved remarkable success in text-to-image generation tasks; however, the role of initial noise has been rarely explored. In this study, we identify specific regions within the initial noise image, termed trigger patches, that play a key role for object generation in the resulting images. Notably, these patches are “universal” and can be generalized across various positions, seeds, and prompts. To be specific, extracting these patches from one noise and injecting them into another noise leads to object generation in targeted areas. We identify these patches by analyzing the dispersion of object bounding boxes across generated images, leading to the development of a posterior analysis technique. Furthermore, we create a dataset consisting of Gaussian noises labeled with bounding boxes corresponding to the objects appearing in the generated images and train a detector that identifies these patches from the initial noise. To explain the formation of these patches, we reveal that they are outliers in Gaussian noise, and follow distinct distributions through two-sample tests. Finally, we find the misalignment between prompts and the trigger patch patterns can result in unsuccessful image generations. The study proposes a reject-sampling strategy to obtain optimal noise, aiming to improve prompt adherence and positional diversity in image generation.

## 1 Introduction

Figure: Figure 1: Illustration: The first row shows images generated from one seed. And we can identify the “trigger patch” located in the red box that tend to induce the generation of the object. If we inject the trigger patch into another noise, there will be objects in the position of the injection place in the images generated by the mixed noise.
Refer to caption: x1.png

In recent years, diffusion models have revolutionized the field of text-to-image generation (Saharia et al., ; Rombach et al., ; Dhariwal and Nichol, ; Nichol et al., ; Ho and Salimans, ). However, these models often fail to accurately adhere to the prompts, frequently generating objects with specific positions or attributes regardless of the input text (Chefer et al., ; Hertz et al., ; Wang et al., ). Although various methods aimed at enhancing control over the generation process have been introduced, including modifying the denoising process (Balaji et al., ), manipulating cross-attention layers (Hertz et al., ; Feng et al., ), and retraining models using layout-image pairs (Zheng et al., ; Zhang et al., ; Voynov et al., ), an important question still left answered that why is the generation process so difficult to control?

In this paper, we show that Gaussian noise in the diffusion process plays a crucial role in image generation. Specifically, we discover the existence of trigger patches – distinct patches in the noise space that trigger the generation of objects in the diffusion model. By moving the trigger patch to a different position, the corresponding object will likely move to that location. Furthermore, this trigger effect also exists across various prompts—the same trigger patch can initiate the generation of different objects, depending on the given prompt. These phenomena are illustrated in Figure 1: when replacing the target patch within another initial noise with the trigger patch, the injection position would generate an object. Identifying the location of trigger patches can provide insights into where objects will be generated without running the diffusion process. Moreover, moving/removing trigger patches can achieve certain image editing effects.

How can we find trigger patches? To give a quantitative way to identify trigger patches, we first propose a posterior analysis approach based on the following intuition: given a specific initial noise, if all the objects are confined to a specific location regardless of the prompts, there must be a trigger patch in the corresponding position. Hence, we define “trigger entropy” based on the variance of coordinates of detected objects in the generated images. But can we detect trigger patches without actually running a diffusion process? We answer this question affirmatively by training a “trigger patch detector”, which functions similarly to an object detector but operates in the noise space. Our trigger patch detector achieves an mAP50 of 0.325 on the validation set(^1^11Faster R-CNN Ren et al. () achieves a mAP50 of 0.596 on COCO validation set Lin et al. ().), revealing that trigger patches possess distinct properties.

So what makes trigger patches special? We hypothesize that the trigger patches are outliers within the Gaussian noise. We perform a two-sample test comparing the trigger patches to randomly selected noise patches and confirm that they follow distinct distributions. In particular, more effective trigger patches show greater divergence from the standard Gaussian distribution. To further support our claim, we design some handcrafted trigger patches shifted from the original distribution and validate that they effectively trigger objects at corresponding positions generated images.

Finally, we demonstrate two applications of trigger patches. For scenarios where positional bias is desired, such as when location information is specified in the prompt, we show that finding noises with trigger patches at the target location can significantly boost the generation success rate from 57.08% to 83.64%. Conversely, for applications where location bias is undesirable, such as when location diversity of generated objects is preferred, we demonstrate that using our proposed detector to "purify" the noise can significantly increase generation diversity.

## 2 Existance of Trigger Patches and How to Find Them

### 2.1 Prelimiaries

#### Denoising Diffusion Probabilistic Models(DDPM)

DDPM Ho et al. () is a kind of generative model, which achieves great performance on high-quality image synthesis. The inference process initiates with the standard Gaussian noise $x_{T}$ and iteratively applies the model to progressively denoise it back towards the natural image $x_{0}$ that subjects to the real data distribution.

#### Classifer-free guidance for conditional generation

Text-to-image diffusion models incorporate classifier-free context information into the reverse diffusion process via cross-attention layers. Specifically, at each sampling step, the denoising error is calculated by adjusting the conditional error with an unconditional error, factored by a guidance strength.

Figure: Figure 2: Heatmap of generated objects on two different noises. The left one has a trigger patch while the right one does not.
Refer to caption: x2.png

### 2.2 Definition of the trigger patch

Where will a diffusion model position an object in the generated images? In this section, we show that the initial noise takes an important role in generated objects’ location. Specifically, we identify regions within the initial noise, termed “trigger patches,” that largely determine the object location. Formally, a trigger patch is a patch in the noise space with the following properties: (1) Triggering Effect: When it presents in the initial noise $Z_{0}$, the trigger patch consistently induces object generation at its corresponding location; (2) Universality Across Prompts: The same trigger patch can trigger the generation of various objects, depending on the given prompt.

Fig 2
illustrates the existence of trigger patches and demonstrates their universality across prompts. For a fixed initial noise, we generate 25 images with various prompts, and then detect the object in each generated image. Summing the object masks and normalizing the result yields a heatmap, where each pixel represents the probability of an object appearing at that location.
Fig 2 demonstrates the heatmap for two different noises. For the left one, the bounding boxes are consistently aligned on the left side, indicating the presence of a trigger patch that consistently leads to object generation at that location. Conversely, the right heatmap has no such an obvious pattern, suggesting no trigger patch in that particular noise.

### 2.3 Identifying trigger patch: a posterior analysis

In this subsection, we propose a posterior analysis to identify and define trigger patches. Intuitively, we generate a bunch of images using the same noise and calculate a posterior metric called “trigger entropy” to measure the degree of dispersion of the object bounding boxes in the generated images. A lower entropy indicates a higher likelihood that a patch is a trigger patch, as shown in Fig 3. We also conduct experiments to assess the efficacy of patches at various levels of trigger entropy in generating objects across different categories and initial noises.

Figure: Figure 3: Illustration: Each row shows five images generated from one seed. The patch in the bottom row has the strongest effectiveness in inducing the generation of the object, while the objects in the top row are dispersed. So there must exist a strong trigger patch in the orange bounding box in the bottom row noise.
Refer to caption: x3.png

#### Dataset

We generate a large-scale dataset consisting of initial noises paired with the bounding boxes of objects in the corresponding images. Initially, we select five classes from the COCO dataset: “stop sign, bear, sports ball, handbag, and apple.” We then prompt ChatGPT to generate five unique sentences for each class, ensuring each sentence features only one object to prevent duplicates. We sample 20,000 Gaussian noises and use diffusion models to generate images based on these noises and prompts. A pre-trained object detector from MMDetection Chen et al. () is then applied to identify the object bounding boxes, which are resized from the image space to the latent space. Only the bounding box with the highest score and correct object label is retained for each image. Please refer to Appendix A for more details.

#### Metric

After obtaining the coordinates of the bounding boxes $\{({x}_{1},{y}_{1},{x}_{2},{y}_{2})\}$, we can define a posterior metric about the effectiveness of the regions in inducing objects, termed “trigger entropy”. For each initial noise, the more concentrated the boxes are, the smaller trigger entropy it has. To avoid the bias of the object size, we compute the center point of each object bounding box ${x}_{c}=\frac{{x}_{1}+{x}_{2}}{2}$ and ${y}_{c}=\frac{{y}_{1}+{y}_{2}}{2}$. Then the entropy of the patch can be defined based on the variance of the box centers:

$$ $\displaystyle\mathcal{H}(X)=\frac{1}{2}\left(\frac{1}{n}\sum_{i=1}^{n}(x_{c_{i }}-\bar{x}_{c})^{2}+\frac{1}{n}\sum_{i=1}^{n}(y_{c_{i}}-\bar{y}_{c})^{2}\right)$ (1) $$

where $\>\bar{x}_{c}=\frac{1}{n}\sum_{i=1}^{n}x_{c_{i}},\>\bar{y}_{c}=\frac{1}{n}\sum
_{i=1}^{n}y_{c_{i}}$, and $i$ is the box index.
So, the more entropy a region has, the less effective it is in determining the objects’ locations.

#### Dataset Statistics

We then compute the trigger entropy of all the 20,000 noises and plot the histograms in Fig 6. We first study a trivial case, where we compute the trigger entropy based on the boxes of one class, “sports ball”, and five prompts about this class. Then for a more general one, we compute the trigger entropy based on all 5 classes and 25 prompts to see if the metric can generalize well across various prompts and classes. As shown in the Figure, nearly 10% noises in the first group have an entropy near 0. In other words, for nearly 2,000 noises, sports balls always show up in almost the same place across the five images generated from an initial noise, indicating a strong trigger patch over that place.

Figure: Figure 4: Trigger Entropy Distribution on the created dataset. Randomly selected bounding boxes as a baseline.
Refer to caption: x4.png

To further explore the characteristics of the trigger patches within an initial noise, we randomly select a noise from the dataset and plot the center points of the detected bounding boxes in Fig 6. We can see that it is possible that multiple trigger patches exist within a single noise sample. Consequently, the posterior metric, which is based on the variance of all bounding boxes, may fail to capture the trigger patches in such scenarios, which will be further addressed in Sec 2.4. Moreover, the trigger patch does not depend on the specific prompt — both trigger patches in the figure can generate baseball gloves (purple points) and bears (green points). These experiments confirm that our trigger patches are universal.

#### Trigger Injection

To verify these patches with low trigger entropy are indeed trigger patches, we design an experiment to test if these patches can still take effect when injected into another noise. In particular, we replace an arbitrary patch in a noise map with the trigger patch and then use the blended noise for generation. A successful injection is characterized by the detected bounding box occupying more than 75 percent of the trigger patch region. Then we define the injection success rate (ISR) as the ratio of successful injection cases to the total number of cases. We sort the patches in our dataset by trigger entropy and select one every two thousand for this test. We do the injection experiment with 200 new random noises. There are two baselines as follows. 1) Resampling: Resample Gaussian noise for the target region maintaining the same mean and variance. 2) Random: Select a random patch within a source noise, which might overlap with the trigger patch in the source noise. Figure 3 illustrates that the Injection Success Rates (ISRs) of most trigger patches exceed those of the Resampling (0.08) and Random (0.01) baselines, confirming the efficacy of the trigger patches identified by our posterior entropy. Additionally, a lower trigger entropy correlates with a higher ISR, suggesting that the trigger patches with low entropy are particularly effective in determining object locations.

#### Trigger-Prompt Interaction

In the previous paragraph, we examine the object position information contained in trigger patches. The analysis thus far raises a subsequent question: What happens when the prompts also contain positional information, and how do the prompt and noise interact with each other when they have aligned and contradicted object positions? To explore this, we design experiments to investigate the interplay between the trigger patches and the prompts. In particular, we design prompts with the format of “a coco class name on the right side”. Then we select three noises: 1) Aligned: with a strong trigger patch on the right, 2) Contradicted: with a strong trigger patch on the left, and 3) Dispersed: with trigger patches dispersed throughout the image. After viewing the generated images, we divided them into four groups: 1) Aligned: The position of the object is aligned with the prompt guidance (On the right side). 2) Contradicted: The position of the object contradicts with the prompt guidance (On the left side). 3) Duplicated: the generated image has two objects on both sides. 4) Hard to judge (Occupying the entire picture, failed generation, or in the middle of the image).

**Table 1: Diversity Results**
| Noise | Aligned (%) | Contradicted (%) | Duplicated (%) | Hard to judge (%) |
| --- | --- | --- | --- | --- |
| Aligned | 63.5 | 6.3 | 6.3 | 23.9 |
| Contradicted | 35.0 | 32.5 | 8.8 | 23.7 |
| Dispersed | 25.0 | 10.0 | 11.3 | 53.7 |

The main findings are as follows. Table 1 demonstrates that the trigger patches significantly influence the final positions of objects. When the prompt and trigger patches are contradictory, 32.5% of objects adhere to the trigger patches, while only 35.0% follow the prompt’s guidance, highlighting the prevalence of failed generations due to conflicts between the prompt and initial noise about where to position objects. Notably, when the prompt and trigger patches are aligned, 63.5% of objects are accurately positioned. These results indicate the potential to manipulate trigger patches for controlled image generation, as demonstrated in Section 4.2.

### 2.4 Detecting trigger patches directly from noise

The above posterior method requires generating images to identify trigger patches. Can we detect the trigger patches without running the diffusion process? To answer this question, we try to train a trigger patch detector, which functions similarly to an object detector but operates in the noise space.

Figure: Figure 7: Permuted Data: We permuted the annotations associated with the noise samples. Initially, in the top row, Noise One was labeled with Annotation One, and Noise Two with Annotation Two. After permutation, shown in the bottom row, Noise One is now labeled with Annotation Two, and Noise Two with Annotation One. Ideally, in scenarios with a strong bias, permuting the annotations should have minimal or no impact on the final results. This is because, in both permuted and unpermuted datasets, the bounding boxes remain centrally located within the image.
Refer to caption: x7.png

#### Dataset

We divide 20,000 random noises into a training set (17,500), a validation set (1,000), and a test set (1,500). Subsequently, we modify the trigger patch annotations (obtained by using the COCO object detector Li et al. () in the image space) to create four distinct datasets, the details of which are presented in Table 2. The Augmented dataset uses bounding boxes of all the 25 prompts, while the Restricted only uses those of the class “sports ball”. In the Class-Specific dataset, the model is required to output the class labels of the trigger patch. Additionally, we craft a dataset with permuted annotations to serve as a baseline to mitigate the effects of model and prompt biases. In particular, model positional bias, often caused by an unbalanced training dataset with all the objects appearing in one place, can lead to generated objects frequently appearing in specific image areas, typically the center. As Fig 7 shows, if model bias is predominant, such that all bounding boxes are centralized, the training outcomes on the Permuted dataset should align with those from the Restricted dataset.

**Table 2: Dataset Description**
| Dataset | Classes | Annotations per noise | Output class labels | Permuted annotations |
| --- | --- | --- | --- | --- |
| Restricted | Sports ball | 5 = 1 $\times$ 5 | $\times$ | $\times$ |
| Augmented | All | 25 = 5 $\times$ 5 | $\times$ | $\times$ |
| Class-Specific | All | 25 = 5 $\times$ 5 | $\checkmark$ | $\times$ |
| Permuted | Sports ball | 5 = 1 $\times$ 5 | $\times$ | $\checkmark$ |

#### Results

We utilize the MMDetection repository Chen et al. () to train our trigger patch detector. Please refer to Appendix B for more details. The results can be seen in Table 3. Our detector on Restricted achieves the mAP50 of 0.325, surpassing the Permuted baseline by 0.124. Such evidence eliminates the influence of the model bias and prompt bias, verifying that the model has learned to locate the trigger patches from initial noises. Notably, the results on the Augmented dataset show that the trigger patches can generalize across different text prompts and provide a foundation for the applications of our detector in various scenarios. Meanwhile, the detector on dataset Class-Specific shows degenerated performance, indicating that the trigger patches are ignorant of the classes. In other words, these patches can only determine where objects are generated, not what to generate. This confirms our finding in Fig 6 that the same patch can trigger different objects, depending on what is given in the prompt.

**Table 3: Main results: Training a detector to anticipate object positions from initial noise.**
| Dataset | Restricted | Augmented | Class-Specific | Randomized |
| --- | --- | --- | --- | --- |
| mAP50 | 0.325 | 0.333 | 0.091 | 0.201 |

## 3 What contributes to the formation of trigger patches

In this part, we propose a potential explanation for the existence of trigger patches. While previous work Guo et al. (); Sun et al. (); Zheng et al. () mainly focuses on the cross-attention maps and analyzes the interactions between specific noise, prompts, and models, we hypothesize that these trigger patches are typical outliers in the sampled noise, and have minimal correlation with prompts. Furthermore, we propose a method to synthesize trigger patches with great success.

### 3.1 Two-sample test

Figure: Figure 8: Energy Distance
Refer to caption: x8.png

We perform an energy-based two-sample test, which measures the distance between the distributions of two samples by computing the sum of pairwise Euclidean distances among all sample points Székely and Rizzo (). Meanwhile, it provides a $p$-value, which statistically quantifies the extent to which the distributions differ from each other. A low $p$-value (typically less than 0.05) suggests that the two sets of samples are not subjected to the same distribution. To test our hypothesis that the trigger patches are outliers in the initial noises, we divide 20,000 noises into ten groups according to the order of Trigger Entropy. Each group has 2,000 noises, and the first group has the lowest Trigger Entropy. Then we refer to the annotations, compute the center point of each bounding box, and extract the trigger patches with a fixed size 24$\times$24 around the center. Following these steps, we obtain a list of trigger patches for each group. We then create ten negative groups by randomly selecting a patch of 24$\times$24 in the same noise. Additionally, we craft a control group by randomly selecting patches of the same size. The results show that all the $p$-values between trigger patch groups and negative prompts are 0.0, while the $p$-value between the negative prompts and the control group is 0.938. Hence, the trigger patches and those random patches in the negative groups are from different distributions. Furthermore, we examine the relationship between the energy distance of trigger patches from negative patches and the trigger entropy, as illustrated in Figure 8. This figure reveals a clear negative correlation: the greater the deviation of a patch from the original distribution, the more likely it is to be a trigger patch characterized by low trigger entropy. This observation again supports our hypothesis that these trigger patches are outliers within the noise.

### 3.2 Hand-crafted trigger patches

If the trigger patches are indeed outliers, it may be feasible to construct certain signals that deviate from a normal Gaussian distribution to serve as artificially created trigger patches. To this end, we conduct experiments to test artificial trigger patches with various non-Gaussian signals.

- 1.
Natural trigger patches: We extract the trigger patches with the lowest trigger entropy from the 20,000 noise samples.
- 2.
Resampling baseline: We resample Gaussian noise maintaining the same mean and variance to establish a baseline.
- 3.
Random baseline: We randomly select 25 sets, each consisting of four numbers, from a range of 512. These numbers are interpreted as the coordinates for the final detected bounding boxes, upon which we compute entropy. This baseline is designed to simulate scenarios where each patch has an equal probability of generating an object.
- 4.
Shifted Gaussian: We sample Gaussian noises with altered standard deviation (std) so the resultant noise follows a different Gaussian from the diffusion models’ default noises.
- 5.
Sine Function: We create sinusoidal noise patches by firstly using a function that applies a sine transformation to each coordinate axis $(x,y,z)$ and then summing up the values. We then add them to an initial noise via interpolation as follows,
$\displaystyle\overline{P_{(x,y,z)}}=\sin(\theta)\cdot\left[\sin(\frac{2\pi x}{
l_{x}})+\sin(\frac{2\pi y}{l_{y}})+\sin(\frac{2\pi z}{l_{z}})\right]+\cos(
\theta)\cdot P_{(x,y,z)},$
(2)
where $P_{(x,y,z)}$ is the pixel value of the original patch at position $(x,y,z)$, $l_{x}$, $l_{y}$ and $l_{z}$ are the widths of the trigger patch, and $\theta$ is the interpolation parameter. In our case, $l_{x}$ $l_{y}$ and $l_{z}$ are 24, 24 and 4, respectively.

The results are displayed in Table 4. Natural trigger patches achieved a success rate of 44.5%, which exceeds the rates of randomly selected bounding boxes and the resampling of the region by 42.5% and 36.0%, respectively. Notably, Sin Function patches yield comparable results when moderate interpolation parameters are set, achieving an ISR of 49%. When the interpolation parameter $\theta$ is set at 0.15$\cdot\frac{\pi}{2}$, it achieves a significantly high ISR of 81.0%. However, this setting also causes image distortion. Interestingly, sampling Gaussian noise with a larger standard deviation appears to be more effective in inducing trigger patches than using a smaller one, verifying that these trigger patches might be considered outliers.

**Table 4: Main results on the injection experiments. The higher the ISR, the better. The left major column shows the ISRs for the baseline methods: Random, Resampling, and Natural. The middle major column shows the results for the shifted Gaussian method with different standard deviations(STD). The right major column shows the results for the Sine Function with different interpolation weights.**
| Baselines | Shifted Gaussian | Sine Function |  |  |  |
| --- | --- | --- | --- | --- | --- |
|  | ISR(%) | STD | ISR(%) | $\theta$($\cdot\frac{\pi}{2}$) | ISR(%) |
| Random | 1.0 | 0.8 | 8.5 | 0.08 | 33.5 |
| Resampling | 8.5 | 1.2 | 29.0 | 0.10 | 49.0 |
| Natural | 44.5 | 1.5 | 90.0 | 0.15 | 81.0 |

## 4 Applications

The ability to detect trigger patches enhances control over object locations in generated images, opening the door to numerous applications. Here, we demonstrate two such applications: 1) In scenarios where the prompt does not have positional information, we aim to increase the positional diversity of the generated images. 2) Conversely, when the prompt includes explicit positional guidance, our goal is to ensure that the generated images follow the provided directions. It is important to note that manipulating trigger patches alone may not deliver state-of-the-art results. Our main objective is to demonstrate that even such a straightforward approach can achieve reasonable performance, highlighting the significant role that trigger patches play in the generation process.

### 4.1 Enhanced location diversity by removing trigger patches

#### Background

Researchers have observed various biases in diffusion models, including gender bias Luccioni et al. () and color bias Orgad et al. (). However, position bias, which is the tendency for objects to consistently appear in the same locations across different generations, has received minimal attention. This type of bias has significant implications, particularly in synthetic data generation using diffusion models. For instance, when generating an automobile dataset, a model exhibiting position bias might consistently place roadblocks in the left-bottom corner of the image, leading to skewed data. Moreover, such a bias can affect the diversity of generated images in applications like ChatGPT, where similar images are produced for varied prompts due to the presence of trigger patches with low trigger entropy in the initial noise.

#### Method

To mitigate this, we have developed a method involving the use of the detector for reject sampling. This process begins with the detection of trigger patches in the initial noise. If the confidence scores of the bounding boxes exceed a predefined threshold, the region within the box is flagged for regeneration. Our approach is designed to ensure that the noise used for generation is “pure” and has no strong trigger patches that could confine object placement.

#### Baselines

Although researchers have studied the positional bias in GAN-based generative models Choi et al. (), no counterpart works have been found on the diffusion models. Focusing on the role of initial noise, Initno Guo et al. () may be the most related one, though it needs the specific prompt for each generation process to take effect. Furthermore, we establish another Control group by generating images using standard methods without reject-sampling. Additionally, we select Random bounding boxes of size 24$\times$24 from the initial noise. This approach simulates a scenario where all pixels have an equal probability of generating an object, which is our target.

#### Metrics and Coniguration

We calculate the average entropy for the bounding boxes in these groups to assess the impact of our method on diversity and positional bias. The entropy is calculated as outlined in Equation (1), with higher values indicating greater diversity. Our experimental setup includes generating images from 10 random prompts described by ChatGPT, followed by image generation using diffusion models. Please refer to the Appendix C for more details. The objects’ bounding boxes are identified using a COCO detector, and entropy calculations are conducted on the bounding boxes with confidence scores over 0.75. We set the rejection threshold for the confidence score of the detector as 0.6 and conducted our experiments using 1000 different seeds.

**Table 5: Diversity Results**
| Methods | Control | Initno | Ours | Random |
| --- | --- | --- | --- | --- |
| Entropy | 135.97 | 139.89 | 171.84 | 170.64 |

As we can see from the table, images generated by our methods show great diversity in position, with an entropy of 171.84, surpassing the control group by 31.95, very close to the pure random outputs, which is 170.64. Meanwhile, Initno shows bad performance with an entropy of 139.89, which is behind ours by a large margin.

### 4.2 Better prompt following by injecting trigger patches

#### Background and Methods

Research indicates that diffusion models often struggle to adhere to the positional information specified in prompts. This issue is typically due to the appearance of trigger patches in unintended locations. For instance, a prominent trigger patch on the left side of an image can conflict with a prompt like “a dog on the left", resulting in generation failures. To address this, we propose a reject-sampling technique to obtain an optimal initial noise where trigger patches align with the prompt requirements even before generation. Specifically, we continue to resample noises until the center point of the bounding box, which scores highest according to our detector, is positioned within the area targeted by the prompt.

#### Baselines and Settings

Our methodology is compared against Initno Guo et al. () and a baseline model that does not utilize reject-sampling. To assess our method’s effectiveness, we design 10 prompts incorporating the words right or left and generate 500 images for each prompt. We employ a pre-trained COCO detector to verify whether the objects are correctly positioned as indicated by the prompt and calculate the guidance success rate (GSR) based on the proportion of correctly positioned objects to the total number of cases. Please refer to Appendix D for more details.

#### Results

Table  6 illustrates that our method, relying solely on the initial noise, achieves an impressive guidance success rate (GSR) of 83.64%.

**Table 6: Diversity Results**
| Methods | Control | Initno | Ours |
| --- | --- | --- | --- |
| GSR(%) | 57.08 | 61.08 | 83.64 |

## 5 Related Work

#### Initial noise

In DDIM Song et al. (), the final image is determined by the model parameters, the text prompt, and the initial noise. While the model parameters and text prompts have been extensively researched, the initial noise remains relatively under-explored. Mao et al. () first highlights that initial noises exhibit distinct preferences for certain layouts and analyze this phenomenon through the lens of cross-attention. Sun et al. () utilized an inverted reference image with finite inversion steps to incorporate valuable spatial awareness, leading to a new framework for controllable image generation. Guo et al. () attributed failed generation cases to ’bad initial noise’ and proposed optimizing the initial noise via cross-attention to achieve better results.

Building on these studies, our research focuses on the role of initial noise. Unlike previous works that qualitatively suggest the presence of positional information in initial noise, we provide evidence for the existence of trigger patches that tend to generate specific objects by defining a metric to quantitatively assess the effectiveness of these patches. Additionally, we propose that these trigger patches are universal and capable of generalizing across different positions, prompts, and background noises. While prior research primarily examines noise from a cross-attention perspective, we discover that the intriguing properties might stem from the statistical characteristics of these patches, which are outliers within the initial noise. Finally, we identify significant applications in enhancing positional diversity. While previous studies mainly addressed biases related to gender, color, and texture, our findings reveal that noise with strong trigger patches can introduce positional bias.

#### Types of objection detection

Object detection is a fundamental computer vision technique that identifies and locates objects in digital images and videos. Various detection networks have been developed for different application scenarios, such as static images Ren et al. (), video frames Wojke et al. (), depth images Reading et al. (), point clouds Qi et al. (), sequential data Lea et al. (), and multi-channel images Chen et al. ().
However, we propose a novel and counter-intuitive approach: using pure Gaussian noise as the input, the model is trained to learn from these noises and extract patches with intriguing properties. To the best of our knowledge, this is the first study to propose such an approach.

## 6 Limitations

We have not thoroughly explored scenarios where one noise sample contains multiple trigger patches and have limited our dataset to five classes and 25 prompts due to computational constraints. A more diverse, large-scale dataset is planned for future research.

## 7 Conclusion

In this study, we have uncovered specific trigger patches within the initial noise that are likely to induce object generation. We subsequently developed a detector capable of identifying these trigger patches from the initial noise prior to the generation process. We characterized these trigger patches as outliers within Gaussian noise and conducted experiments to validate this classification. Finally, we show two potential applications for our detector, both of which have demonstrated excellent performance. We leave more applications for future work.

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## Appendix A Dataset Crafting

#### Prompts

The baseball glove waits by the fence.
A young athlete breaks in a new baseball glove.
A baseball glove rests on the dugout bench.
His baseball glove hangs by the door.
A baseball glove is left on the fence during practice.
A grizzly bear fishes in a rushing river.
A bear cub explores the forest with curiosity.
A bear catches a fish in the river.
A black bear forages for berries in the woods.
A bear sniffs the forest floor.
A fashionable handbag complements an elegant outfit.
A woman carries a stylish handbag on her shoulder.
A handbag rests on a cafe table during lunch.
A handbag holds essentials for a day of shopping.
A handbag adds a pop of color to a monochrome look.
A sports ball is caught in a fence.
A sports ball lies forgotten under a tree.
A sports ball sits on a sandy beach.
A sports ball rests on a grassy land.
A sports ball stands out on a muddy field.
A red stop sign halts traffic at an intersection.
A stop sign stands alone on a country road.
A stop sign is covered in a layer of snow.
A stop sign is adorned with event flyers.
A stop sign stands at the entrance to a neighborhood.

#### filtering

We filter the annotations with a confidence score higher than 0.75 and the label is right.

## Appendix B Detector training

We utilized the mmdetection repository Chen et al. []. Our approach incorporated Generalized Focal Loss Li et al. [] and a Resnet101 architecture Chen et al. [] expanded to 4$\times$ width to accommodate the 4-channel inputs of the initial noises. We adhered to the COCO dataset configurations provided by the repository. During training, we observed that strong data augmentation techniques significantly impaired performance, leading us to eliminate Flip and Random Resize functions. We conducted our training on four NVIDIA GTX 1080 Ti graphics cards using 17.5k noise samples and report the mean Average Precision (mAP) at 50% threshold on the 1k validation dataset.

#### Configs

We utilized the mmdetection repository Chen et al. []. Our approach incorporated Generalized Focal Loss Li et al. [] and a Resnet101 architecture Chen et al. [] expanded to 4$\times$ width to accommodate the 4-channel inputs of the initial noises. We adhered to the COCO dataset configurations provided by the repository. During training, we found that strong data augmentation techniques degenerate the performance greatly. During training, we observed that strong data augmentation techniques significantly impaired performance, leading us to eliminate Flip and Random Resize Transormations. We conducted our training on four NVIDIA GTX 1080 Ti graphics cards using 17.5k noise samples and reported the mean Average Precision (mAP) at 50% threshold on the 1k validation dataset.

## Appendix C Enhanced location diversity by removing trigger patches

:

#### Prompts we use

The golden sunlight filters through the dense canopy of the forest, casting dappled shadows on the moss-covered ground.
A red bicycle leans against a gnarled oak tree, its wheels slightly caked with mud from the morning’s ride.
Nearby, a picnic table is set with a checkered cloth, and atop it rests a basket filled with fresh fruit and sandwiches.
A frisbee lies forgotten on the grass, a few feet away from a sleeping dog with its fur glistening in the sun.
In the background, a kite dances in the sky, its bright colors a stark contrast against the blue expanse above.
A laptop is open on the table, displaying vibrant images of nature, momentarily abandoned for the allure of the outdoors.
A baseball glove and ball sit on the bench, remnants of a game played in the spirit of friendly competition.
A traffic cone marks the end of a nearby trail, signaling caution to the cyclists and hikers passing by.
A fire hydrant stands at the edge of the clearing, its red paint chipped but vibrant, a silent guardian of safety.
As the day wanes, the street lights begin to flicker on, their glow adding a soft luminescence to the tranquil scene.

## Appendix D Better prompt following by injecting trigger patches

#### Prompts we use

a sports ball in the left,
a cow in the left,
an apple in the left,
a bicycle in the left,
a vase in the left
a sports ball in the right,
a cow in the right,
an apple in the right,
a bicycle in the right,
a vase in the right

## Appendix E Resources

We use 4 1080 Ti for generating and evaluating.

## Peer Reviews

confidence: 3
contribution: 3
initial_rating: 8
presentation: 3
questions: Please address the questions / concerns in the weaknesses section.
soundness: 3
strengths: 1. The concept of "trigger patches" in the diffusion generation process is both interesting and useful, as it enhances the controllability of the generation.
2. The experiments and analyses are thorough and comprehensive.
3. The writing is clear and intuitive.
summary: In the paper, the authors introduce the concept of "trigger patches," which are specific regions within the initial noise image that determine the positional information in object generation. They present a method for localizing these trigger patches, provide analyses to validate their correctness, and demonstrate two applications.
weaknesses: 1. In the evaluation of the second application (Sec 5.2), only "left" and "right" are considered. Is it possible to include more fine-grained positional information, such as "left-down"?
2. In the introduction, it is mentioned that "moving/removing trigger patches can achieve certain image editing effects." Including some image editing results in the experimental section would support this claim.
3. In cases where "trigger patches" and prompts are aligned, the positional generation accuracy is 63.5%. What factors contribute to the failures in the remaining cases? Can the authors provide a failure analysis?

---

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: See weakness.
soundness: 3
strengths: 1.The insight is interesting.

2.The authors not only demonstrated the existence of trigger patch noise through experiments but also provided a method for its detection. Additionally, the authors thoroughly explored the effects of multiple trigger patch noises, examined the relationship between trigger patch noise and prompt guidance, and investigated the generalization capabilities of trigger patch noise.

3.I believe that the proposed concept of trigger patch noise has the potential to advance research and development in the field of controllable generation.
summary: This article introduces the intriguing concept of trigger patch noise. The authors first demonstrate the existence of trigger patch noise, then propose a method using neural networks to detect this noise in initial noise. They experimentally verify the unique characteristics of trigger patch noise and explore its potential applications, such as controlling object generation position by embedding trigger patch noise into the initial noise.
weaknesses: 1.The experiment was conducted with only five object categories. Can trigger patch noise be generalized to a broader range of object categories? This could provide insights into its robustness across diverse applications.

2.Does trigger patch noise commonly exist within any randomly sampled Gaussian noise? Additionally, if multiple trigger patch noises are present in a single Gaussian noise, what criteria should be used to select the most effective trigger patch noise?

3.In the training process of the trigger patch noise detector, how do you define the ground truth for trigger patch noise? Providing a detailed algorithm or clarification of this aspect would be valuable. Furthermore, does every one of the 17,000 noises in the training set contain trigger patch noise?

4.There seems to be an impact on image realism when inserting trigger patch noise. How significant is this effect, and are there any methods to mitigate it? (The BLIP-Text results in Table 11)

5.The detection accuracy of trigger patch noise reported in the paper appears somewhat limited. Are there plans or suggestions for enhancing detection performance?

6.What would be the effect of inserting multiple (e.g., three) trigger patch noises? Additionally, when aiming to control the size of the generated object, does resizing the trigger patch noise (e.g., scaling) still yield the intended effect?

7.Can the trigger patch noise work for DiT models?

---

confidence: 3
contribution: 3
initial_rating: 5
presentation: 3
questions: 1. Please test on wider range of objects as well as datasets or find the trigger patches on different locations of the dataset instead of the right edge of the photo.
2. Please provide the qualitative values for image quality and observe the trade-off between diversity and image quality from the proposed rejection sampling method.
3. Please provide more comprehensive evaluations on diversity such as FID/Recall.
soundness: 3
strengths: Strength:
1. The paper provides an interesting point of view on diffusion sampling
2. The new sampling methods help to increase the diversity
summary: The work finds out that there are some locations in the image frame where the diffusion often gets biased. These locations are marked as trigger patches. An object detector is trained to detect these patches before the sampling process. After that, rejection sampling is used to reject samples with trigger patches to obtain the better generative image diversity.
weaknesses: Weaknesses:
1. According to Figure 1 and Figure 3, the trigger patches are always in the right part of the image and only applicable to some objects. The whole paper also only focuses on some round objects like balls and tennis balls. This results in the question of generalization of the work. Whether or not this phenomenon will happen across datasets or with different objects?
2. The experimental results do not show the quantitative values to measure the output quality. There could be a trade-off between diversity and quality according to the new rejection sampling. 
3. The current diversity result is not standard in generative measures such as FID/Recall.

---

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: See the weaknesses.
soundness: 3
strengths: Thanks for the authors` efforts. I find this paper very interesting, and the experimental section is quite comprehensive. It has provided me with many insights and considerations.

1. The paper is well-organized, and the presentation of this paper is very good.

2. The motivation of this paper is clear, and it first explores the influence of positional bias in the initial noise. I think the experiments are quite comprehensive. I think this paper is valuable.

3. Some experiment results are very attractive, and they have sparked a lot of my thoughts and reflections.
summary: This paper explores the influence of initial noise in the text-to-image generation tasks. They identify specific regions within the initial noise termed as trigger patches, which contribute to the positional bias in the generated images. In order to automatically discover the trigger patches, the authors train a detector. Next, the authors explore several special and interesting attributes of trigger patches, and discover the differences between the random patch within the initial noise and trigger patch. At last, based on the discoveries, the authors design two speical applications for trigger patch.
weaknesses: Although, from my perspective, this paper is good, I think it still has several drawbacks:

Presentation:

1. In line 231, "As shown in the Figure", missing reference to the Figure. In line 293, missing (2) before "Can noises with multiple ...". In line 417, ":" is missing after "Control", and the first word after ":"， should be lowercase.  In line 1070, "Please refer to the Fig F.2 for visualized results.", I can not find the Fig.F2.

2. In Figure 13, the prompt is not consistent with the provided images.

3. All intuitive images in the main paper only contain five concepts. Can the authors provide more visualization results?

Methods and Experiments:

1. For the evaluation metrics, the authors only utilize the CLIP. I think it is crucial to utilize some human preference models like PickScore, HPSv2 to evaluate the quality of the generated images.

2. The dataset constructed by the authors only contains five single concepts, consisting of 500K samples. How do the authors ensure that whether the trigger patches exist beyond these five prompts, and the detector trained in this manner can recognize other concepts? Besides, I think the construction of the dataset is resource-consuming.

3. The authors claim that low entropy ISR will be higher; however, Table 6 shows that certain mid-entropy ISRs are also quite high. How should the authors explain this phenomenon?

4. All of the main results are conducted only in Stable Diffusion v2. Can the authors provide the existence of the trigger patches in other diffusion models?

5. Experiment results in Table 5 reveal “Random” can surpass "Initno" and "Attend-and-Excite". This phenomenon is very strange because as far as I know, both of them optimize the noise during the reverse process. They should be higher than "Random"?

6. The experiment results in Generalization part raise my concerns. From the results presented in Table 8, it seems that trigger patch injection is only effective with deterministic samplers, showing no impact on stochastic samplers. The authors also default to using a deterministic sampler. Besides, based on the results in Table 10, why is the gap reduction so pronounced across other models? If the initial noise inherently carries positional bias, then its performance across different diffusion models should be similar. However, the experimental results seem to contradict the notion that the trigger patch is universal.

Meta-review: This paper explores the influence of initial noise in the text-to-image generation task, and proposes the concept of triggle patches that play a key role in inducing object generation in the resulting images. All reviewers agree the insight of triggle patches are interesting, and the discovery of triggle patches helps to advance research in the field of controllable generation. The AC agrees with the reviewers and recommend accept.

Decision: Accept (Poster)