Generating sequences of images, or video, introduces significant complexity compared to synthesizing static images. While the core principles of GANs and diffusion models still apply, generating video demands explicit modeling of temporal dynamics to ensure coherence and realistic motion across frames. Simply generating frames independently often results in flickering artifacts or inconsistent object appearances, failing to capture the smooth transitions inherent in real-world video.

Challenges Unique to Video Synthesis

Extending generative models from images to video presents several distinct hurdles:

Temporal Coherence: Maintaining consistency in object identity, appearance, background, and motion across frames is arguably the primary challenge. Generated videos must look like a continuous recording, not a sequence of unrelated images.
Modeling Motion: Accurately capturing the physics and patterns of movement is difficult. This includes both global scene changes and the articulation of objects or characters within the scene.
High Dimensionality: Video data adds a temporal dimension to the already high-dimensional spatial data of images, dramatically increasing the complexity of the data distribution to be learned. A short video clip contains vastly more information than a single image.
Long-Range Dependencies: Events or appearances in early frames can influence much later frames. Models need mechanisms to capture these long-term temporal relationships.
Computational Cost: Training video models requires substantially more memory and computation than image models due to the sequence length and often the need for specialized architectures like 3D convolutions or recurrent layers.

Extending Generative Models for Video

Several strategies have been developed to adapt GANs and diffusion models for video generation, moving beyond naive frame-by-frame synthesis:

3D Convolutional Networks: Just as 2D convolutions are effective for spatial patterns in images, 3D convolutions can simultaneously process spatial information within frames and temporal information across frames. Both the generator and discriminator in a Video GAN (VGAN) can employ 3D convolutional layers to learn spatio-temporal features directly from video data. The generator maps a latent vector $z$ to a sequence of frames, while the discriminator takes a sequence of frames and outputs a probability of it being real.
$G: z \rightarrow \{x_1, x_2, ..., x_T\}$ $D: \{x_1, x_2, ..., x_T\} \rightarrow [0, 1]$
Here, $x_t$ represents the frame at time $t$ , and $T$ is the total number of frames in the sequence.
Recurrent Architectures: Recurrent Neural Networks (RNNs), particularly LSTMs or GRUs, can be integrated into the generator. For instance, an RNN can process a sequence of latent vectors, where each output state informs the generation of the corresponding frame, often in conjunction with convolutional layers. This explicitly models the sequential nature of video.
Factored Latent Spaces: Some architectures attempt to disentangle factors of variation, such as separating a latent representation for static content (e.g., object appearance, background) from a representation for dynamic motion. MoCoGAN (Motion and Content decomposed GAN) is an example where a content code is sampled once per sequence, while a sequence of motion codes drives the frame-to-frame changes.

A common structure for a Video GAN, potentially using separate latent codes for content and motion, processed by spatio-temporal generator and discriminator networks.

Temporal Attention: Similar to their use in image generation, attention mechanisms can be adapted for video to model long-range dependencies across time and space. Transformers, leveraging self-attention, are increasingly being used for video generation tasks.

Video Diffusion Models

Diffusion models can also be extended to video. The core idea remains the same: gradually noise the data (forward process) and learn to reverse this process (denoising).

Forward Process: Gaussian noise is typically added independently to each frame at each diffusion timestep, potentially with shared noise schedules across frames.
$q(x_{1:T}^k | x_{1:T}^{k-1}) = \prod_{t=1}^T \mathcal{N}(x_t^k; \sqrt{1-\beta_k} x_t^{k-1}, \beta_k I)$
where $x_{1:T}^k = \{x_1^k, ..., x_T^k\}$ is the sequence of frames at diffusion step $k$ , and $\beta_k$ is the noise variance schedule.
Reverse Process: The denoising network must predict the noise added (or the less noisy video) across the entire sequence. This typically involves spatio-temporal network architectures, often U-Nets modified with 3D convolutions or incorporating temporal attention layers to process information across both space and time.
$p_\theta(x_{1:T}^{k-1} | x_{1:T}^k) = \mathcal{N}(x_{1:T}^{k-1}; \mu_\theta(x_{1:T}^k, k), \Sigma_\theta(x_{1:T}^k, k))$
The network $\mu_\theta$ (parameterized by $\theta$ ) predicts the mean of the distribution for the previous step's video sequence given the current noisy sequence $x_{1:T}^k$ and the step $k$ .

Conditioning video diffusion models (e.g., for text-to-video or action-conditional generation) follows similar principles as in image diffusion, often using classifier guidance or classifier-free guidance adapted to handle sequential inputs and outputs. Due to the high computational load, techniques like Latent Diffusion, where diffusion operates in a compressed latent space, are also being adapted for video.

Evaluating Generated Video

Evaluating video quality requires assessing both per-frame realism and temporal characteristics. Metrics like Fréchet Inception Distance (FID) have been extended to video as Fréchet Video Distance (FVD). FVD uses features extracted from a pre-trained video classification network (like I3D) to compare the distribution of generated videos to real videos, considering both appearance and motion. Qualitative assessment remains important, scrutinizing videos for flickering, motion artifacts, and overall temporal smoothness.

Generating high-quality, temporally consistent video is an active area of research. While extending image generation techniques provides a foundation, addressing the unique challenges of temporal modeling often requires specialized architectures and training strategies, alongside considerable computational resources.