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Authors:
(1) Yuwei Guo, The Chinese University of Hong Kong;
(2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author;
(3) Anyi Rao, Stanford University;
(4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory;
(5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory;
(6) Yu Qiao, Shanghai Artificial Intelligence Laboratory;
(7) Maneesh Agrawala, Stanford University;
(8) Dahua Lin, Shanghai Artificial Intelligence Laboratory;
(9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction 2 Work Related 3 Preliminary AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.3 Ablative Study 5.4 Controllable Generation 6 Conclusion 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 6 CONCLUSION In this paper, we present AnimateDiff, a practical pipeline directly turning personalized text-toimage (T2I) models for animation generation once and for all, without compromising quality or losing pre-learned domain knowledge. To accomplish this, we design three component modules in AnimateDiff to learn meaningful motion priors while alleviating visual quality degradation and enabling motion personalization with a lightweight fine-tuning technique named MotionLoRA. Once trained, our motion module can be integrated into other personalized T2Is to generate animated images with natural and coherent motions while remaining faithful to the personalized domain. Extensive evaluation with various personalized T2I models also validates the effectiveness and generalizability of our AnimateDiff and MotionLoRA. Furthermore, we demonstrate the compatibility of our method with existing content-controlling approaches, enabling controllable generation without incurring additional training costs. Overall, AnimateDiff provides an effective baseline for personalized animation and holds significant potential for a wide range of applications. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Authors: Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Work Related 2 Work Related 3 Preliminary 3 Preliminary AnimateDiff AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.2 Qualitative Comparison 5.3 Ablative Study 5.3 Ablative Study 5.4 Controllable Generation 5.4 Controllable Generation 6 Conclusion 6 Conclusion 7 Ethics Statement 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 8 Reproducibility Statement, Acknowledgement and References 6 CONCLUSION In this paper, we present AnimateDiff, a practical pipeline directly turning personalized text-toimage (T2I) models for animation generation once and for all, without compromising quality or losing pre-learned domain knowledge. To accomplish this, we design three component modules in AnimateDiff to learn meaningful motion priors while alleviating visual quality degradation and enabling motion personalization with a lightweight fine-tuning technique named MotionLoRA. Once trained, our motion module can be integrated into other personalized T2Is to generate animated images with natural and coherent motions while remaining faithful to the personalized domain. Extensive evaluation with various personalized T2I models also validates the effectiveness and generalizability of our AnimateDiff and MotionLoRA. Furthermore, we demonstrate the compatibility of our method with existing content-controlling approaches, enabling controllable generation without incurring additional training costs. Overall, AnimateDiff provides an effective baseline for personalized animation and holds significant potential for a wide range of applications. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

How AnimateDiff Transforms T2I Models into High-Quality Animation Generators with MotionLORA

Authors:
(1) Yuwei Guo, The Chinese University of Hong Kong;
(2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author;
(3) Anyi Rao, Stanford University;
(4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory;
(5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory;
(6) Yu Qiao, Shanghai Artificial Intelligence Laboratory;
(7) Maneesh Agrawala, Stanford University;
(8) Dahua Lin, Shanghai Artificial Intelligence Laboratory;
(9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction 2 Work Related 3 Preliminary AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.3 Ablative Study 5.4 Controllable Generation 6 Conclusion 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 5.4 CONTROLLABLE GENERATION. The separated learning of visual content and motion priors in AnimateDiff enables the direct application of existing content control approaches for controllable generation. To demonstrate this capability, we combined AnimateDiff with ControlNet (Zhang et al., 2023) to control the generation with extracted depth map sequence. In contrast to recent video editing techniques (Ceylan et al., 2023; Wang et al., 2023a) that employ DDIM (Song et al., 2020) inversion to obtain smoothed latent sequences, we generate animations from randomly sampled noise. As illustrated in Figure 8, our results exhibit meticulous motion details (such as hair and facial expressions) and high visual quality. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Authors: Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Work Related 2 Work Related 3 Preliminary 3 Preliminary AnimateDiff AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.2 Qualitative Comparison 5.3 Ablative Study 5.3 Ablative Study 5.4 Controllable Generation 5.4 Controllable Generation 6 Conclusion 6 Conclusion 7 Ethics Statement 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 8 Reproducibility Statement, Acknowledgement and References 5.4 CONTROLLABLE GENERATION. The separated learning of visual content and motion priors in AnimateDiff enables the direct application of existing content control approaches for controllable generation. To demonstrate this capability, we combined AnimateDiff with ControlNet (Zhang et al., 2023) to control the generation with extracted depth map sequence. In contrast to recent video editing techniques (Ceylan et al., 2023; Wang et al., 2023a) that employ DDIM (Song et al., 2020) inversion to obtain smoothed latent sequences, we generate animations from randomly sampled noise. As illustrated in Figure 8, our results exhibit meticulous motion details (such as hair and facial expressions) and high visual quality. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

AnimateDiff Combines with ControlNet for Precise Motion Control and High-Quality Video Generation

Authors:
(1) Yuwei Guo, The Chinese University of Hong Kong;
(2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author;
(3) Anyi Rao, Stanford University;
(4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory;
(5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory;
(6) Yu Qiao, Shanghai Artificial Intelligence Laboratory;
(7) Maneesh Agrawala, Stanford University;
(8) Dahua Lin, Shanghai Artificial Intelligence Laboratory;
(9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction 2 Work Related 3 Preliminary AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.3 Ablative Study 5.4 Controllable Generation 6 Conclusion 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 5.3 ABLATIVE STUDY Domain adapter. To investigate the impact of the domain adapter in AnimateDiff, we conducted a study by adjusting the scaler in the adapter layers during inference, ranging from 1 (full impact) to 0 (complete removal). As illustrated in Figure 6, as the scaler of the adapter decreases, there is an improvement in overall visual quality, accompanied by a reduction in the visual content distribution learned from the video dataset (the watermark in the case of WebVid (Bain et al., 2021)). These results indicate the successful role of the domain adapter in enhancing the visual quality of AnimateDiff by alleviating the motion module from learning the visual distribution gap. Motion module design. We compare our motion module design of the temporal Transformer with its full convolution counterpart, which is motivated by the fact that both designs are widely employed in recent works on video generation. We replace the temporal attention with 1D temporal convolution and ensured that the two model parameters were closely aligned. As depicted in supplementary materials, the convolutional motion module aligns all frames to be identical but does not incorporate any motion compared to the Transformer architecture. Efficiency of MotionLoRA. The efficiency of MotionLoRA in AnimateDiff was examined in terms of parameter efficiency and data efficiency. Parameter efficiency is crucial for efficient model training and sharing among users, while data efficiency is essential for real-world applications where collecting an adequate number of reference videos for specific motion patterns may be challenging. To investigate these aspects, we trained multiple MotionLoRA models with varying parameter scales and reference video quantities. In Fig. 7, the first two samples demonstrate that MotionLoRA is capable of learning new camera motions (e.g., zoom-in) with a small parameter scale while maintaining comparable motion quality. Furthermore, even with a modest number of reference videos (e.g., N = 50), the model successfully learns the desired motion patterns. However, when the number of reference videos is excessively limited (e.g., N = 5), significant degradation in quality is observed, suggesting that MotionLoRA encounters difficulties in learning shared motion patterns and instead relies on capturing texture information from the reference videos. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Authors: Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Work Related 2 Work Related 3 Preliminary 3 Preliminary AnimateDiff AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.2 Qualitative Comparison 5.3 Ablative Study 5.3 Ablative Study 5.4 Controllable Generation 5.4 Controllable Generation 6 Conclusion 6 Conclusion 7 Ethics Statement 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 8 Reproducibility Statement, Acknowledgement and References 5.3 ABLATIVE STUDY Domain adapter. To investigate the impact of the domain adapter in AnimateDiff, we conducted a study by adjusting the scaler in the adapter layers during inference, ranging from 1 (full impact) to 0 (complete removal). As illustrated in Figure 6, as the scaler of the adapter decreases, there is an improvement in overall visual quality, accompanied by a reduction in the visual content distribution learned from the video dataset (the watermark in the case of WebVid (Bain et al., 2021)). These results indicate the successful role of the domain adapter in enhancing the visual quality of AnimateDiff by alleviating the motion module from learning the visual distribution gap. Domain adapter. Motion module design. We compare our motion module design of the temporal Transformer with its full convolution counterpart, which is motivated by the fact that both designs are widely employed in recent works on video generation. We replace the temporal attention with 1D temporal convolution and ensured that the two model parameters were closely aligned. As depicted in supplementary materials, the convolutional motion module aligns all frames to be identical but does not incorporate any motion compared to the Transformer architecture. Motion module design. Efficiency of MotionLoRA. The efficiency of MotionLoRA in AnimateDiff was examined in terms of parameter efficiency and data efficiency. Parameter efficiency is crucial for efficient model training and sharing among users, while data efficiency is essential for real-world applications where collecting an adequate number of reference videos for specific motion patterns may be challenging. To investigate these aspects, we trained multiple MotionLoRA models with varying parameter scales and reference video quantities. In Fig. 7, the first two samples demonstrate that MotionLoRA is capable of learning new camera motions (e.g., zoom-in) with a small parameter scale while maintaining comparable motion quality. Furthermore, even with a modest number of reference videos (e.g., N = 50), the model successfully learns the desired motion patterns. However, when the number of reference videos is excessively limited (e.g., N = 5), significant degradation in quality is observed, suggesting that MotionLoRA encounters difficulties in learning shared motion patterns and instead relies on capturing texture information from the reference videos. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Ablative Study on Domain Adapter, Motion Module Design, and MotionLoRA Efficiency

Authors:
(1) Yuwei Guo, The Chinese University of Hong Kong;
(2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author;
(3) Anyi Rao, Stanford University;
(4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory;
(5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory;
(6) Yu Qiao, Shanghai Artificial Intelligence Laboratory;
(7) Maneesh Agrawala, Stanford University;
(8) Dahua Lin, Shanghai Artificial Intelligence Laboratory;
(9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction 2 Work Related 3 Preliminary AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.3 Ablative Study 5.4 Controllable Generation 6 Conclusion 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 5 EXPERIMENTS We implement AnimateDiff upon Stable Diffusion V1.5 and train motion module using the WebVid10M (Bain et al., 2021) dataset. Detailed configurations can be found in supplementary materials. 5.1 QUALITATIVE RESULTS Evaluate on community models. We evaluated the AnimateDiff with a diverse set of representative personalized T2Is collected from Civitai (2022). These personalized T2Is encompass a wide range of domains, thus serving as a comprehensive benchmark. Since personalized domains in these T2Is only respond to certain “trigger words”, we abstain from using common text prompts but refer to the model homepage to construct the evaluation prompts. In Fig. 4, we show eight qualitative results of AnimateDiff. Each sample corresponds to a distinct personalized T2I. In the second row of Figure 1, we present the outcomes obtained by integrating AnimateDiff with MotionLoRA to achieve shot type controls. The last two samples exhibit the composition capability of MotionLoRA, achieved by linearly combining the individually trained weights. Compare with baselines. In the absence of existing methods specifically designed for animating personalized T2Is, we compare our method with two recent works in video generation that can be adapted for this task: 1) Text2Video-Zero (Khachatryan et al., 2023) and 2) Tune-a-Video (Wu 7 et al., 2023). We also compare AnimateDiff with two commercial tools: 3) Gen-2 (2023) for textto-video generation, and 4) Pika Labs (2023) for image animation. The results are shown in Fig. 5. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Authors: Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Work Related 2 Work Related 3 Preliminary 3 Preliminary AnimateDiff AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.2 Qualitative Comparison 5.3 Ablative Study 5.3 Ablative Study 5.4 Controllable Generation 5.4 Controllable Generation 6 Conclusion 6 Conclusion 7 Ethics Statement 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 8 Reproducibility Statement, Acknowledgement and References 5 EXPERIMENTS We implement AnimateDiff upon Stable Diffusion V1.5 and train motion module using the WebVid10M (Bain et al., 2021) dataset. Detailed configurations can be found in supplementary materials. 5.1 QUALITATIVE RESULTS Evaluate on community models. We evaluated the AnimateDiff with a diverse set of representative personalized T2Is collected from Civitai (2022). These personalized T2Is encompass a wide range of domains, thus serving as a comprehensive benchmark. Since personalized domains in these T2Is only respond to certain “trigger words”, we abstain from using common text prompts but refer to the model homepage to construct the evaluation prompts. In Fig. 4, we show eight qualitative results of AnimateDiff. Each sample corresponds to a distinct personalized T2I. In the second row of Figure 1, we present the outcomes obtained by integrating AnimateDiff with MotionLoRA to achieve shot type controls. The last two samples exhibit the composition capability of MotionLoRA, achieved by linearly combining the individually trained weights. Compare with baselines. In the absence of existing methods specifically designed for animating personalized T2Is, we compare our method with two recent works in video generation that can be adapted for this task: 1) Text2Video-Zero (Khachatryan et al., 2023) and 2) Tune-a-Video (Wu 7 et al., 2023). We also compare AnimateDiff with two commercial tools: 3) Gen-2 (2023) for textto-video generation, and 4) Pika Labs (2023) for image animation. The results are shown in Fig. 5. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

How AnimateDiff Brings Personalized T2Is to Life with Efficient Motion Modeling

Authors:
(1) Yuwei Guo, The Chinese University of Hong Kong;
(2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author;
(3) Anyi Rao, Stanford University;
(4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory;
(5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory;
(6) Yu Qiao, Shanghai Artificial Intelligence Laboratory;
(7) Maneesh Agrawala, Stanford University;
(8) Dahua Lin, Shanghai Artificial Intelligence Laboratory;
(9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction 2 Work Related 3 Preliminary AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.3 Ablative Study 5.4 Controllable Generation 6 Conclusion 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 4.3 ADAPT TO NEW MOTION PATTERNS WITH MOTIONLORA While the pre-trained motion module captures general motion priors, a question arises when we need to effectively adapt it to new motion patterns such as camera zooming, panning and rolling, etc., with a small number of reference videos and training iterations. Such efficiency is essential for users who cannot afford expensive pre-training costs but would like to fine-tune the motion module for specific effects. Here comes the last stage of AnimateDiff, also dubbed as MotionLoRA (Fig. 3), an efficient fine-tuning approach for motion personalization. Considering the architecture of the motion module and the limited number of reference videos, we add LoRA layers to the self-attention layers of the motion module in the inflated model described in Sec. 4.2, then train these LoRA layers on the reference videos of new motion patterns. We experiment with several shot types and get the reference videos via rule-based data augmentation. For instance, to get videos with zooming effects, we augment the videos by gradually reducing (zoom-in) or enlarging (zoom-out) the cropping area of video frames along the temporal axis. We demonstrate that our MotionLoRA can achieve promising results even with as few as 20 ∼ 50 reference videos, 2,000 training iterations (around 1 ∼ 2 hours) as well as about 30M storage space, enabling efficient model tuning and sharing among users. Benefited by the low-rank property, MotionLoRA also has the composition capability. Namely, individually trained MotionLoRA models can be combined to achieve composed motion effects at inference time. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Authors: Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Work Related 2 Work Related 3 Preliminary 3 Preliminary AnimateDiff AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.2 Qualitative Comparison 5.3 Ablative Study 5.3 Ablative Study 5.4 Controllable Generation 5.4 Controllable Generation 6 Conclusion 6 Conclusion 7 Ethics Statement 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 8 Reproducibility Statement, Acknowledgement and References 4.3 ADAPT TO NEW MOTION PATTERNS WITH MOTIONLORA While the pre-trained motion module captures general motion priors, a question arises when we need to effectively adapt it to new motion patterns such as camera zooming, panning and rolling, etc., with a small number of reference videos and training iterations. Such efficiency is essential for users who cannot afford expensive pre-training costs but would like to fine-tune the motion module for specific effects. Here comes the last stage of AnimateDiff, also dubbed as MotionLoRA (Fig. 3), an efficient fine-tuning approach for motion personalization. Considering the architecture of the motion module and the limited number of reference videos, we add LoRA layers to the self-attention layers of the motion module in the inflated model described in Sec. 4.2, then train these LoRA layers on the reference videos of new motion patterns. We experiment with several shot types and get the reference videos via rule-based data augmentation. For instance, to get videos with zooming effects, we augment the videos by gradually reducing (zoom-in) or enlarging (zoom-out) the cropping area of video frames along the temporal axis. We demonstrate that our MotionLoRA can achieve promising results even with as few as 20 ∼ 50 reference videos, 2,000 training iterations (around 1 ∼ 2 hours) as well as about 30M storage space, enabling efficient model tuning and sharing among users. Benefited by the low-rank property, MotionLoRA also has the composition capability. Namely, individually trained MotionLoRA models can be combined to achieve composed motion effects at inference time. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Adapting Motion Patterns Efficiently with MotionLoRA in AnimateDiff

Authors:
(1) Yuwei Guo, The Chinese University of Hong Kong;
(2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author;
(3) Anyi Rao, Stanford University;
(4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory;
(5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory;
(6) Yu Qiao, Shanghai Artificial Intelligence Laboratory;
(7) Maneesh Agrawala, Stanford University;
(8) Dahua Lin, Shanghai Artificial Intelligence Laboratory;
(9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction 2 Work Related 3 Preliminary AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.3 Ablative Study 5.4 Controllable Generation 6 Conclusion 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 4.2 LEARN MOTION PRIORS WITH MOTION MODULE To model motion dynamics along the temporal dimension on top of a pre-trained T2I, we must 1) inflate the 2-dimensional diffusion model to deal with 3-dimensional video data and 2) design a sub-module to enable efficient information exchange along the temporal axis. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Authors: Authors: (1) Yuwei Guo, The Chinese University of Hong Kong; (2) Ceyuan Yang, Shanghai Artificial Intelligence Laboratory with Corresponding Author; (3) Anyi Rao, Stanford University; (4) Zhengyang Liang, Shanghai Artificial Intelligence Laboratory; (5) Yaohui Wang, Shanghai Artificial Intelligence Laboratory; (6) Yu Qiao, Shanghai Artificial Intelligence Laboratory; (7) Maneesh Agrawala, Stanford University; (8) Dahua Lin, Shanghai Artificial Intelligence Laboratory; (9) Bo Dai, The Chinese University of Hong Kong and The Chinese University of Hong Kong. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Work Related 2 Work Related 3 Preliminary 3 Preliminary AnimateDiff AnimateDiff 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.1 Alleviate Negative Effects from Training Data with Domain Adapter 4.2 Learn Motion Priors with Motion Module 4.2 Learn Motion Priors with Motion Module 4.3 Adapt to New Motion Patterns with MotionLora 4.3 Adapt to New Motion Patterns with MotionLora 4.4 AnimateDiff in Practice 4.4 AnimateDiff in Practice 5 Experiments and 5.1 Qualitative Results 5 Experiments and 5.1 Qualitative Results 5.2 Qualitative Comparison 5.2 Qualitative Comparison 5.3 Ablative Study 5.3 Ablative Study 5.4 Controllable Generation 5.4 Controllable Generation 6 Conclusion 6 Conclusion 7 Ethics Statement 7 Ethics Statement 8 Reproducibility Statement, Acknowledgement and References 8 Reproducibility Statement, Acknowledgement and References 4.2 LEARN MOTION PRIORS WITH MOTION MODULE To model motion dynamics along the temporal dimension on top of a pre-trained T2I, we must 1) inflate the 2-dimensional diffusion model to deal with 3-dimensional video data and 2) design a sub-module to enable efficient information exchange along the temporal axis. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Mastering Motion Dynamics in Animation with Temporal Transformers

A mysterious botnet, identified by the user-agent string Mozilla/5.0 (X11; Linux x86_64), is aggressively scraping WordPress websites at an alarming rate, flagrantly disregarding the crawl delay directives set in the  robots.txt file. The botnet has been found to be causing significant server strain, bypassing web administrators' efforts to control access and protect their site resources. Despite the bot's user-agent string mimicking a legitimate Linux browser, its bad behavior is anything but lawful. Not only does it ignore robots.txt instructions, but it also carries out non-stop scraping activities that severely impact the performance and security of affected websites. The unregulated scraping can lead to slowed website loading times and increased bandwidth consumption. IP Addresses and ASN Sources Involved The IP addresses behind this botnet appear to originate from multiple autonomous system numbers (ASNs), primarily hosted by less-reputable service providers. The IPs exhibit coordinated behavior, systematically scraping WordPress websites with no regard for the implemented crawl-delay directives. The ASNs and their affiliated IP addresses are: ASN 13886 - Cloud-South


ASN 21769 - AS-COLOAM


ASN 263735 - Sociedad Buena Hosting, S.A.


ASN 52393 - Corporacion Dana S.A. 185.199.117.126
216.10.7.2
104.233.51.70
104.249.4.61
186.179.1.64
181.177.71.218
185.195.215.202
185.193.73.239
104.239.116.255
185.199.118.137
185.193.72.244
216.10.3.36
186.179.11.6
181.177.70.128
104.239.115.2
186.179.10.14
104.249.5.146
185.199.116.245
104.233.54.62
185.207.97.112
185.199.116.218
181.177.71.59
104.249.0.172
104.233.49.164
185.188.78.129
216.10.2.44
104.233.48.205
216.10.6.143
104.249.1.226
185.196.191.240
67.227.122.211
185.195.221.166
181.177.79.165
186.179.25.11
185.199.117.248
185.195.220.198
104.239.114.195
181.177.66.111
67.227.127.113
185.205.196.57
199.168.122.42
186.179.27.9
185.193.75.105
216.10.3.10
216.10.2.161
185.188.77.24
104.233.48.70
185.188.79.15
186.179.2.186
181.177.72.76
216.10.6.205
186.179.13.13
181.177.78.227
181.177.72.12
181.177.79.141
186.179.25.210
104.233.49.36
104.249.3.157
104.239.117.199
104.233.48.52
104.233.51.106
216.10.3.78
216.10.0.49
185.207.99.161
67.227.120.127
67.227.121.26
104.233.55.225
104.249.3.194
185.195.220.41
181.177.71.84
104.233.48.111
104.249.2.46
181.177.67.170
104.249.2.195
186.179.13.80
67.227.124.74
104.239.116.151
104.239.119.180
185.195.221.180
104.249.2.99
104.239.114.190
104.239.117.112
181.177.71.49
67.227.121.109
199.168.121.93
185.195.223.14
181.177.67.30
181.177.76.63
181.177.77.79
181.177.66.29
181.177.77.197
186.179.24.252
185.196.188.94
181.177.76.62
216.10.7.75
181.177.68.33
186.179.11.165
181.177.71.188
185.195.213.87
185.193.74.97
67.227.122.57
185.196.189.63
216.10.1.142
199.168.122.193
186.179.2.117
181.177.72.134
181.177.66.212
185.188.77.122
185.207.96.121
199.168.121.246
104.249.0.31
185.195.222.160 Potential Mitigation Strategies Web administrators are urged to monitor their logs for suspicious activity involving the Mozilla/5.0 (X11; Linux x86_64) user-agent string and IPs associated with the above ASNs. Immediate actions to consider include: Blocking or rate-limiting the offending IPs through firewall rules.


Implementing CAPTCHA systems for suspicious traffic.


Using bot protection plugins or services such as Cloudflare to prevent excessive scraping. The persistence of this botnet highlights the importance of continually refining web security measures to protect digital assets from unauthorized data scraping and potential attacks. This unknown botnet's activity is a pressing issue for WordPress site owners, and if left unchecked, its presence could lead to server overloads, data leaks, or even downtime for many websites. Interestingly, despite the aggressive nature of this botnet, none of the associated IPs have been flagged or reported in popular databases like AbuseIPDB. Even more surprising, these IPs are not natively blocked by Cloudflare’s managed rules, which typically catch such malicious behavior early on. This suggests that the botnet is currently flying under the radar, operating in a gray zone of anonymity. The lack of detection and reporting raises concerns about how sophisticated and stealthy this botnet may be. For now, it seems to be an entirely unknown entity in the cybersecurity landscape. However, it does seem look like it is scraping WordPress content. A mysterious botnet, identified by the user-agent string Mozilla/5.0 (X11; Linux x86_64) , is aggressively scraping WordPress websites at an alarming rate, flagrantly disregarding the crawl delay directives set in the  robots.txt file. The botnet has been found to be causing significant server strain, bypassing web administrators' efforts to control access and protect their site resources. Mozilla/5.0 (X11; Linux x86_64) Despite the bot's user-agent string mimicking a legitimate Linux browser, its bad behavior is anything but lawful. Not only does it ignore robots.txt instructions, but it also carries out non-stop scraping activities that severely impact the performance and security of affected websites. The unregulated scraping can lead to slowed website loading times and increased bandwidth consumption. robots.txt IP Addresses and ASN Sources Involved The IP addresses behind this botnet appear to originate from multiple autonomous system numbers (ASNs), primarily hosted by less-reputable service providers. The IPs exhibit coordinated behavior, systematically scraping WordPress websites with no regard for the implemented crawl-delay directives. The ASNs and their affiliated IP addresses are: ASN 13886 - Cloud-South ASN 21769 - AS-COLOAM ASN 263735 - Sociedad Buena Hosting, S.A. ASN 52393 - Corporacion Dana S.A. ASN 13886 - Cloud-South ASN 13886 - Cloud-South ASN 13886 - Cloud-South ASN 21769 - AS-COLOAM ASN 21769 - AS-COLOAM ASN 21769 - AS-COLOAM ASN 263735 - Sociedad Buena Hosting, S.A. ASN 263735 - Sociedad Buena Hosting, S.A. ASN 263735 - Sociedad Buena Hosting, S.A. ASN 52393 - Corporacion Dana S.A. ASN 52393 - Corporacion Dana S.A. ASN 52393 - Corporacion Dana S.A. 185.199.117.126
216.10.7.2
104.233.51.70
104.249.4.61
186.179.1.64
181.177.71.218
185.195.215.202
185.193.73.239
104.239.116.255
185.199.118.137
185.193.72.244
216.10.3.36
186.179.11.6
181.177.70.128
104.239.115.2
186.179.10.14
104.249.5.146
185.199.116.245
104.233.54.62
185.207.97.112
185.199.116.218
181.177.71.59
104.249.0.172
104.233.49.164
185.188.78.129
216.10.2.44
104.233.48.205
216.10.6.143
104.249.1.226
185.196.191.240
67.227.122.211
185.195.221.166
181.177.79.165
186.179.25.11
185.199.117.248
185.195.220.198
104.239.114.195
181.177.66.111
67.227.127.113
185.205.196.57
199.168.122.42
186.179.27.9
185.193.75.105
216.10.3.10
216.10.2.161
185.188.77.24
104.233.48.70
185.188.79.15
186.179.2.186
181.177.72.76
216.10.6.205
186.179.13.13
181.177.78.227
181.177.72.12
181.177.79.141
186.179.25.210
104.233.49.36
104.249.3.157
104.239.117.199
104.233.48.52
104.233.51.106
216.10.3.78
216.10.0.49
185.207.99.161
67.227.120.127
67.227.121.26
104.233.55.225
104.249.3.194
185.195.220.41
181.177.71.84
104.233.48.111
104.249.2.46
181.177.67.170
104.249.2.195
186.179.13.80
67.227.124.74
104.239.116.151
104.239.119.180
185.195.221.180
104.249.2.99
104.239.114.190
104.239.117.112
181.177.71.49
67.227.121.109
199.168.121.93
185.195.223.14
181.177.67.30
181.177.76.63
181.177.77.79
181.177.66.29
181.177.77.197
186.179.24.252
185.196.188.94
181.177.76.62
216.10.7.75
181.177.68.33
186.179.11.165
181.177.71.188
185.195.213.87
185.193.74.97
67.227.122.57
185.196.189.63
216.10.1.142
199.168.122.193
186.179.2.117
181.177.72.134
181.177.66.212
185.188.77.122
185.207.96.121
199.168.121.246
104.249.0.31
185.195.222.160 Potential Mitigation Strategies Web administrators are urged to monitor their logs for suspicious activity involving the Mozilla/5.0 (X11; Linux x86_64) user-agent string and IPs associated with the above ASNs. Immediate actions to consider include: Mozilla/5.0 (X11; Linux x86_64) Blocking or rate-limiting the offending IPs through firewall rules. Implementing CAPTCHA systems for suspicious traffic. Using bot protection plugins or services such as Cloudflare to prevent excessive scraping. Blocking or rate-limiting the offending IPs through firewall rules. Blocking or rate-limiting the offending IPs through firewall rules. Implementing CAPTCHA systems for suspicious traffic. Implementing CAPTCHA systems for suspicious traffic. Using bot protection plugins or services such as Cloudflare to prevent excessive scraping. Using bot protection plugins or services such as Cloudflare to prevent excessive scraping. The persistence of this botnet highlights the importance of continually refining web security measures to protect digital assets from unauthorized data scraping and potential attacks. This unknown botnet's activity is a pressing issue for WordPress site owners, and if left unchecked, its presence could lead to server overloads, data leaks, or even downtime for many websites. Interestingly, despite the aggressive nature of this botnet, none of the associated IPs have been flagged or reported in popular databases like AbuseIPDB. Even more surprising, these IPs are not natively blocked by Cloudflare’s managed rules, which typically catch such malicious behavior early on. This suggests that the botnet is currently flying under the radar, operating in a gray zone of anonymity. The lack of detection and reporting raises concerns about how sophisticated and stealthy this botnet may be. For now, it seems to be an entirely unknown entity in the cybersecurity landscape. However, it does seem look like it is scraping WordPress content. unknown entity

Unknown Botnet Using Mozilla/5.0 (X11; Linux x86_ User Agent Ignoring Crawl Delay on WordPress Sites

Author:
(1) K. Razi Naqvi, Department of Physics, Norwegian University of Science and Technology (NTNU), 7094 Trondheim, Norway Table of Links Abstract and 1 Introduction 2 Preliminary material 3 Comments elicited by the solution to Milne’s problem for B-particles 4 Flux to a spherical trap 5 Molecular motion in liquids 6 Concluding remarks and References 5 Molecular motion in liquids One of the most important and keenly controverted issues dicussed by Hildebrand in his thoughtful and purposely provocative note is the question whether concepts borrowed from the kinetic theory of gases or classical hydrodynamics can be legitimately applied to describe solute diffusion in liquid [30]. The bulk of his criticism is to be found in the last two paragraphs, excerpts from which appear below: Attempts to calculate absolute values of diffusivity have been made by starting from Stokes’ law for a particle settling under the pull of gravity, and extrapolating over the long path to a molecule participating with its neighbors in aimless thermal motions that are never as long as the molecular diameter. Individual molecules are not impelled by a vector force that can serve to measure a “coefficient of friction.” Any such coefficient is fictitious. If molecules were hard spheres, instead of electron clouds with imbedded nuclei, and were sufficiently far apart to justify speaking of binary collisions with linear free paths between them, the probable distance they could be expected to wander from their initial positions could be computed by the formula for a “random walk.” But polyatomic molecules that move less than 10 percent of their diameter require a more sophisticated mathematical formulation. They are in a continual state of soft, slow collision, with constant exchange between translational and internal energy. The random walk in this case is a slow, tipsy reel, without sudden changes of direction. The mathematical problem involved . . . If one is content with the macroscopic description provided by the DE, concepts such as the mean free path and friction coefficient do indeed recede into the background, but not until we have derived a satisfactory boundary condition. If one wants to ascertain the validity of the macroscopic equations, for example the boundary condition for a particular problem, one is obliged to take a microscopic look. Whether one uses the LBE (which speaks of trajectories between separable collisions) or the KKE (which envisages a medium with a given friction coefficient) for delimiting the domain of validity of the macroscopic description is quite immaterial, so long as one can convince oneself that one’s conclusion does not rest on some idiosyncracy of the model; the means would justify the end provided that the end can be reached by some other means as well. This paper is available on arxiv under CC BY 4.0 DEED license. Author: (1) K. Razi Naqvi, Department of Physics, Norwegian University of Science and Technology (NTNU), 7094 Trondheim, Norway Author: Author: (1) K. Razi Naqvi, Department of Physics, Norwegian University of Science and Technology (NTNU), 7094 Trondheim, Norway Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Preliminary material 2 Preliminary material 3 Comments elicited by the solution to Milne’s problem for B-particles 3 Comments elicited by the solution to Milne’s problem for B-particles 4 Flux to a spherical trap 4 Flux to a spherical trap 5 Molecular motion in liquids 5 Molecular motion in liquids 6 Concluding remarks and References 6 Concluding remarks and References 5 Molecular motion in liquids One of the most important and keenly controverted issues dicussed by Hildebrand in his thoughtful and purposely provocative note is the question whether concepts borrowed from the kinetic theory of gases or classical hydrodynamics can be legitimately applied to describe solute diffusion in liquid [30]. The bulk of his criticism is to be found in the last two paragraphs, excerpts from which appear below: Attempts to calculate absolute values of diffusivity have been made by starting from Stokes’ law for a particle settling under the pull of gravity, and extrapolating over the long path to a molecule participating with its neighbors in aimless thermal motions that are never as long as the molecular diameter. Individual molecules are not impelled by a vector force that can serve to measure a “coefficient of friction.” Any such coefficient is fictitious. If molecules were hard spheres, instead of electron clouds with imbedded nuclei, and were sufficiently far apart to justify speaking of binary collisions with linear free paths between them, the probable distance they could be expected to wander from their initial positions could be computed by the formula for a “random walk.” But polyatomic molecules that move less than 10 percent of their diameter require a more sophisticated mathematical formulation. They are in a continual state of soft, slow collision, with constant exchange between translational and internal energy. The random walk in this case is a slow, tipsy reel, without sudden changes of direction. The mathematical problem involved . . . If one is content with the macroscopic description provided by the DE, concepts such as the mean free path and friction coefficient do indeed recede into the background, but not until we have derived a satisfactory boundary condition. If one wants to ascertain the validity of the macroscopic equations, for example the boundary condition for a particular problem, one is obliged to take a microscopic look. Whether one uses the LBE (which speaks of trajectories between separable collisions) or the KKE (which envisages a medium with a given friction coefficient) for delimiting the domain of validity of the macroscopic description is quite immaterial, so long as one can convince oneself that one’s conclusion does not rest on some idiosyncracy of the model; the means would justify the end provided that the end can be reached by some other means as well. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Revisiting Discrepancies in Diffusion Theory: Molecular Motion in Liquids 

Software developers are feeling the heat, and not just because it’s summertime. Even though there is currently a high demand for programmers, the rumor mill is turning, and it’s saying that AI may soon replace developers for a sizable chunk of their common tasks. This may be true of repetitive work and some quality testing, but fortunately, market analysts anticipate that there will be a strong demand for experienced developers in the upcoming years, particularly those who know how to leverage AI. The future may be uncertain, but one thing we do know is: successful developers will require new skills to be valued by many organizations. 3 high-paying roles to apply for today

ETS Enterprise Portfolio Architect – ISD Prin Arch - Cloud, Navy Federal Credit Union, Winchester ($129,100 - $229,925)
Sr R&D Engineer, Lowe's, Kirkland ($163,800 - $311,200)
Senior DevSecOps Engineer, SciTec, Boulder ($125,000 - $168,400) The future looks bright for Rust developers in particular. This language is rising in popularity due to its high performance, safety features, and versatility, and is being adopted by some of the world’s leading tech companies. For ambitious programmers, becoming a Rustacean presents an opportunity to make a mark in a cutting-edge language, and bring home a significant salary too. Let’s take a closer look. Rust 411 Rust is expected to be in great demand as a systems language as it is versatile, and used to develop low-level system components as diverse as operating systems, system utilities, device drivers, game and VR simulation engines, and Internet of Things devices. The language started as a side project for a single Mozilla engineer who intended to create a new programming language that would solve the memory management and allocation issues with C and C++. But later, the open-source software company used Rust as the foundation for a new Firefox browser engine, and a love affair began. Due to its special qualities, Rust is becoming more and more popular, despite not having the same support ecosystem as older programming languages. However, the systems language has advanced quickly in recent years. Rust is unique in that it has an ownership and borrowing system that is just as fast and compact as C and C++, but it provides memory security without the need for garbage collection. In contrast to previous programming languages, Rust guards against memory issues like data races and buffer overflows, and its programmers are protected against mistakes that could result in memory errors by strict data typing constraints. Additionally, its contemporary syntax and overhead-free abstractions have also made a mark. Companies using Rust Rust is becoming more and more popular among businesses of all sizes, due to its distinctive qualities, but this is especially true for safety-critical projects. Its wide range of applications includes network programming, web development, and system programming. In addition, there is a growing need for the system language in the fields of app development, blockchain, Internet of Things, and smart contract programming. Discord, for instance, accelerates its system by utilizing the low-level language. The chat platform's speed increased tenfold after converting to Rust. The programming language was used by Meta to make changes to the internal source code management software that its engineers utilize. Dropbox synchronizes files between user devices and its cloud storage via the system language. Rust is a key part of Microsoft and Amazon’s future, while the U.S. government is even advising to lessen "vulnerabilities at scale," programmers should convert to memory-safe languages like Rust. 3 great tech jobs hiring now

Senior Associate - Software Engineering: Java, Options Clearing Corporation, Chicago
Java Developer, The Hollister Group, Boston
Manager-Data Services, Whisker, Auburn Hills Earning potential According to recent analysis of 342 salaries, a Rust developer in the U.S. makes, on average, $156,000 a year. While the majority of experienced Rustaceans can earn close to $200,000 annually, entry-level positions begin at $121,875 per year – not too shabby. These figures from job titles including Rust compare well with more general software developer job titles. For example, software engineers command $123,594, system engineers $115,184, and developers $112,502. Regionally speaking, Texas and New York both offer the highest salaries to Rust developers at $187,500, followed by Georgia ($175,00) and California ($150,000). Ready to find your next role in tech? Whether you’re a Rust expert or novice or simply want to put your coding expertise to good use, visit the Hackernoon Job Board today By Amanda Kavanagh Software developers are feeling the heat, and not just because it’s summertime. Even though there is currently a high demand for programmers, the rumor mill is turning, and it’s saying that AI may soon replace developers for a sizable chunk of their common tasks. AI This may be true of repetitive work and some quality testing, but fortunately, market analysts anticipate that there will be a strong demand for experienced developers in the upcoming years, particularly those who know how to leverage AI. The future may be uncertain, but one thing we do know is: successful developers will require new skills to be valued by many organizations. 3 high-paying roles to apply for today ETS Enterprise Portfolio Architect – ISD Prin Arch - Cloud, Navy Federal Credit Union, Winchester ($129,100 - $229,925)
Sr R&D Engineer, Lowe's, Kirkland ($163,800 - $311,200)
Senior DevSecOps Engineer, SciTec, Boulder ($125,000 - $168,400) 3 high-paying roles to apply for today 3 high-paying roles to apply for today ETS Enterprise Portfolio Architect – ISD Prin Arch - Cloud, Navy Federal Credit Union, Winchester ($129,100 - $229,925) Sr R&D Engineer, Lowe's, Kirkland ($163,800 - $311,200) Senior DevSecOps Engineer, SciTec, Boulder ($125,000 - $168,400) ETS Enterprise Portfolio Architect – ISD Prin Arch - Cloud, Navy Federal Credit Union, Winchester ($129,100 - $229,925) ETS Enterprise Portfolio Architect – ISD Prin Arch - Cloud, Navy Federal Credit Union, Winchester ($129,100 - $229,925) ETS Enterprise Portfolio Architect – ISD Prin Arch - Cloud, Navy Federal Credit Union, Winchester ($129,100 - $229,925) Sr R&D Engineer, Lowe's, Kirkland ($163,800 - $311,200) Sr R&D Engineer, Lowe's, Kirkland ($163,800 - $311,200) Sr R&D Engineer, Lowe's, Kirkland ($163,800 - $311,200) Senior DevSecOps Engineer, SciTec, Boulder ($125,000 - $168,400) Senior DevSecOps Engineer, SciTec, Boulder ($125,000 - $168,400) Senior DevSecOps Engineer, SciTec, Boulder ($125,000 - $168,400) The future looks bright for Rust developers in particular. This language is rising in popularity due to its high performance, safety features, and versatility, and is being adopted by some of the world’s leading tech companies. Rust For ambitious programmers, becoming a Rustacean presents an opportunity to make a mark in a cutting-edge language, and bring home a significant salary too. Let’s take a closer look. Rust 411 Rust is expected to be in great demand as a systems language as it is versatile, and used to develop low-level system components as diverse as operating systems, system utilities, device drivers, game and VR simulation engines, and Internet of Things devices. The language started as a side project for a single Mozilla engineer who intended to create a new programming language that would solve the memory management and allocation issues with C and C++. But later, the open-source software company used Rust as the foundation for a new Firefox browser engine, and a love affair began. Due to its special qualities, Rust is becoming more and more popular, despite not having the same support ecosystem as older programming languages. However, the systems language has advanced quickly in recent years. Rust is unique in that it has an ownership and borrowing system that is just as fast and compact as C and C++, but it provides memory security without the need for garbage collection. In contrast to previous programming languages, Rust guards against memory issues like data races and buffer overflows, and its programmers are protected against mistakes that could result in memory errors by strict data typing constraints. Additionally, its contemporary syntax and overhead-free abstractions have also made a mark. Companies using Rust Rust is becoming more and more popular among businesses of all sizes, due to its distinctive qualities, but this is especially true for safety-critical projects. Its wide range of applications includes network programming, web development, and system programming. In addition, there is a growing need for the system language in the fields of app development, blockchain, Internet of Things, and smart contract programming. Discord, for instance, accelerates its system by utilizing the low-level language. The chat platform's speed increased tenfold after converting to Rust. The programming language was used by Meta to make changes to the internal source code management software that its engineers utilize. Dropbox synchronizes files between user devices and its cloud storage via the system language. Rust is a key part of Microsoft and Amazon’s future, while the U.S. government is even advising to lessen "vulnerabilities at scale," programmers should convert to memory-safe languages like Rust. 3 great tech jobs hiring now Senior Associate - Software Engineering: Java, Options Clearing Corporation, Chicago
Java Developer, The Hollister Group, Boston
Manager-Data Services, Whisker, Auburn Hills 3 great tech jobs hiring now 3 great tech jobs hiring now Senior Associate - Software Engineering: Java, Options Clearing Corporation, Chicago Java Developer, The Hollister Group, Boston Manager-Data Services, Whisker, Auburn Hills Senior Associate - Software Engineering: Java, Options Clearing Corporation, Chicago Senior Associate - Software Engineering: Java, Options Clearing Corporation, Chicago Senior Associate - Software Engineering: Java, Options Clearing Corporation, Chicago Java Developer, The Hollister Group, Boston Java Developer, The Hollister Group, Boston Java Developer, The Hollister Group, Boston Manager-Data Services, Whisker, Auburn Hills Manager-Data Services, Whisker, Auburn Hills Manager-Data Services, Whisker, Auburn Hills Earning potential According to recent analysis of 342 salaries, a Rust developer in the U.S. makes, on average, $156,000 a year. While the majority of experienced Rustaceans can earn close to $200,000 annually, entry-level positions begin at $121,875 per year – not too shabby. recent analysis recent analysis These figures from job titles including Rust compare well with more general software developer job titles. For example, software engineers command $123,594, system engineers $115,184, and developers $112,502. Regionally speaking, Texas and New York both offer the highest salaries to Rust developers at $187,500, followed by Georgia ($175,00) and California ($150,000). Ready to find your next role in tech? Whether you’re a Rust expert or novice or simply want to put your coding expertise to good use, visit the Hackernoon Job Board today Ready to find your next role in tech? Whether you’re a Rust expert or novice or simply want to put your coding expertise to good use, visit the Hackernoon Job Board today Ready to find your next role in tech? Whether you’re a Rust expert or novice or simply want to put your coding expertise to good use, visit the Hackernoon Job Board today Ready to find your next role in tech? Whether you’re a Rust expert or novice or simply want to put your coding expertise to good use, visit the Hackernoon Job Board today By Amanda Kavanagh By Amanda Kavanagh By Amanda Kavanagh

From Mozilla to Meta, Amazon and Microsoft, Rustaceans Are in Demand Right Now

মোজিলা থেকে মেটা, অ্যামাজন এবং মাইক্রোসফ্ট পর্যন্ত, রাস্টেসিয়ান এখনই চাহিদা রয়েছে৷

Von Mozilla über Meta bis hin zu Amazon und Microsoft sind Rustaceans derzeit gefragt

Desde Mozilla hasta Meta, Amazon y Microsoft, los rustáceos están muy demandados en este momento

De Mozilla à Meta, en passant par Amazon et Microsoft, les Rustaceans sont très demandés en ce moment

मोज़िला से लेकर मेटा, अमेज़न और माइक्रोसॉफ्ट तक, रूसटेसियन की इस समय मांग है

MozillaからMeta、Amazon、Microsoftまで、Rustaceansは現在需要がある

Mozilla에서 Meta, Amazon, Microsoft까지 Rustaceans는 지금 당장 수요가 많습니다.

Da Mozilla à Meta, Amazon e Microsoft, os Rustáceos estão em demanda agora

От Mozilla до Meta, Amazon и Microsoft: Rustaceans сейчас пользуются спросом

Mozilla'dan Meta'ya, Amazon'dan Microsoft'a, Rustacean'lara Şu Anda Talep Var

Từ Mozilla đến Meta, Amazon và Microsoft, Rustaceans đang được săn đón hiện nay

从 Mozilla 到 Meta、亚马逊和微软，Rustaceans 需求旺盛

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