Generate videos end-to-end using normalizing flows instead of diffusion: leverage invertible transformations for exact likelihood computation, eliminate train-test mismatch, and achieve non-iterative sampling with native support for multiple tasks (text-to-video, image-to-video) without fine-tuning.
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Generate videos end-to-end using normalizing flows instead of diffusion: leverage invertible transformations for exact likelihood computation, eliminate train-test mismatch, and achieve non-iterative sampling with native support for multiple tasks (text-to-video, image-to-video) without fine-tuning.
STARFlow-V: Flow-Based Video Generation
While diffusion models dominate video generation through iterative denoising, normalizing flows offer complementary advantages: exact likelihood evaluation, non-iterative sampling, and unified treatment of multiple generation tasks. This skill demonstrates how to implement STARFlow-V, a flow-based video generator that learns invertible transformations mapping video distributions to simple priors.
The core innovation is combining global-local latent structures (compact global temporal context + local spatial detail) with flow-score matching to maintain causality while preserving temporal consistency.
Core Concept
STARFlow-V implements video generation via normalizing flows:
Invertible Transformation: Learn mapping V = g_θ(Z) where Z ~ N(0,I) and g is invertible
Global-Local Structure: Global latent carries temporal context; local blocks preserve spatial detail
Flow-Score Matching: Lightweight denoiser maintains causality without breaking invertibility
End-to-End Training: Direct maximum likelihood estimation via change-of-variables formula
Architecture Overview
Encoder: Maps videos to latent space via variational compression
Global Latent Sequence: Compact representation of temporal dynamics
Local Latent Blocks: Spatial detail information
Flow Model: Invertible transformation mapping prior to latent distribution
The flow-based generation system operates through encoding, flow transformation, and decoding.
1. Implement Invertible Latent Encoder
Create invertible compression mapping videos to latent space.
classInvertibleVideoEncoder(torch.nn.Module):
"""
Encodes videos to latent space with invertible transformation.
Enables exact likelihood computation through change-of-variables formula.
"""def__init__(self, channels=3, hidden_dim=64):
super().__init__()
.channels = channels
.hidden_dim = hidden_dim
.spatial_encoder = torch.nn.Sequential(
InvertibleConv1x1(channels, hidden_dim),
CouplingLayer(hidden_dim, hidden_dim * ),
InvertibleConv1x1(hidden_dim, hidden_dim),
CouplingLayer(hidden_dim, hidden_dim * )
)
.temporal_encoder = torch.nn.Sequential(
TemporalCouplingLayer(hidden_dim, hidden_dim),
TemporalCouplingLayer(hidden_dim, hidden_dim)
)
():
batch, time, c, h, w = video.shape
spatial_latents = []
log_det_sum =
t (time):
frame = video[:, t]
latent, log_det = .spatial_encoder(frame)
spatial_latents.append(latent)
log_det_sum += log_det
spatial_latents = torch.stack(spatial_latents, dim=)
latents, log_det_temporal = .temporal_encoder(spatial_latents)
total_log_det = log_det_sum + log_det_temporal
latents, total_log_det
():
spatial_latents = .temporal_encoder.inverse(latents)
batch, time = spatial_latents.shape[:]
video = []
t (time):
frame_latent = spatial_latents[:, t]
frame = .spatial_encoder.inverse(frame_latent)
video.append(frame)
video = torch.stack(video, dim=)
video
self
self
# Spatial encoder (per-frame)
self
2
2
# Temporal encoder (across frames)
self
def
forward
self, video
"""
Invertible encoding of video to latent space.
Args:
video: (batch, time, channels, height, width)
Returns:
latents: (batch, time, hidden_dim, height, width)
log_det_jacobian: Log determinant of transformation for likelihood
"""
# Encode spatially per frame
0.0
for
in
range
self
1
# Encode temporally
self
return
def
inverse
self, latents
"""
Decode from latent space back to video space (invertible).
"""
# Inverse temporal transform
self
# Inverse spatial transform per frame
2
for
in
range
self
1
return
2. Implement Global-Local Latent Structure
Design latent representation separating temporal dynamics from spatial detail.
classGlobalLocalLatentStructure(torch.nn.Module):
"""
Decomposes video latents into global (temporal) and local (spatial) components.
Reduces error accumulation in autoregressive generation.
"""def__init__(self, latent_dim=256, num_frames=16):
super().__init__()
self.latent_dim = latent_dim
self.num_frames = num_frames
# Global stream: compact temporal sequenceself.global_compressor = torch.nn.Sequential(
torch.nn.Conv3d(latent_dim, latent_dim // 4, kernel_size=(3, 1, 1), padding=(1, 0, 0)),
torch.nn.ReLU(),
torch.nn.Conv3d(latent_dim // 4, latent_dim // 8, kernel_size=(3, 1, 1), padding=(1, 0, 0))
)
# Local stream: per-frame spatial detailself.local_extractor = torch.nn.Sequential(
torch.nn.Conv3d(latent_dim, latent_dim, kernel_size=(1, 3, 3), padding=(0, 1, 1)),
torch.nn.ReLU()
)
defdecompose(self, latents):
"""
Decompose latents into global and local components.
Args:
latents: (batch, time, latent_dim, height, width)
Returns:
global_latent: (batch, global_dim, time) temporal dynamics
local_latent: (batch, time, local_dim, height, width) spatial details
"""# Reshape for 3D convolution
batch, time, dim, h, w = latents.shape
latents_3d = latents.permute(0, 2, 1, 3, 4) # (batch, dim, time, h, w)# Extract global: compress spatial dimensions
global_latent = self.global_compressor(latents_3d)
global_latent = global_latent.mean(dim=(3, 4)) # Average spatial → (batch, global_dim, time)# Extract local: preserve all details
local_latent = self.local_extractor(latents_3d)
local_latent = local_latent.permute(0, 2, 1, 3, 4) # (batch, time, local_dim, h, w)return global_latent, local_latent
defrecombine(self, global_latent, local_latent):
"""
Recombine global and local latents (inverse of decompose).
"""# Expand global to spatial dimensions
batch, global_dim, time = global_latent.shape
_, _, local_dim, h, w = local_latent.shape
global_expanded = global_latent.unsqueeze(-1).unsqueeze(-1)
global_expanded = global_expanded.expand(-1, -1, -1, h, w)
global_expanded = global_expanded.permute(0, 2, 1, 3, 4) # (batch, time, global_dim, h, w)# Combine: scaled addition
combined = local_latent + 0.1 * global_expanded
return combined
3. Implement Normalizing Flow Model
Build the invertible transformation learning flow.
classNormalizingFlowForVideo(torch.nn.Module):
"""
Normalizing flow mapping simple prior to video latent distribution.
Enables exact likelihood computation via change-of-variables formula.
"""def__init__(self, latent_dim=256, num_flows=16):
super().__init__()
self.latent_dim = latent_dim
self.num_flows = num_flows
# Stack of invertible transformationsself.flows = torch.nn.ModuleList([
CouplingFlowLayer(latent_dim, hidden_dim=512)
for _ inrange(num_flows)
])
defforward(self, latents):
"""
Forward pass through flow (encode to prior space).
Args:
latents: (batch, total_latent_dim) flattened latents
Returns:
z: (batch, total_latent_dim) samples from prior
log_det_jacobian: Likelihood adjustment
"""
z = latents
log_det_sum = 0.0for flow inself.flows:
z, log_det = flow(z)
log_det_sum += log_det
return z, log_det_sum
definverse(self, z):
"""
Inverse pass through flow (decode from prior to latent space).
For generation, sample z ~ N(0,I) and apply inverse.
"""
latents = z
# Reverse flow order for inversefor flow inreversed(self.flows):
latents = flow.inverse(latents)
return latents
defsample(self, batch_size, device):
"""
Generate samples from prior and decode through flow.
Args:
batch_size: Number of samples
device: Torch device
Returns:
latents: Decoded samples in latent space
"""# Sample from standard normal prior
z = torch.randn(batch_size, self.latent_dim, device=device)
# Decode through inverse flow
latents = self.inverse(z)
return latents
4. Implement Flow-Score Matching for Causality
Add lightweight denoiser maintaining temporal causality without breaking invertibility.
classFlowScoreMatching(torch.nn.Module):
"""
Lightweight score-matching denoiser that maintains causality.
Applied to latent space for refined generation without breaking invertibility.
"""def__init__(self, latent_dim=256, num_frames=16):
super().__init__()
self.latent_dim = latent_dim
self.num_frames = num_frames
# Causal transformer: only attends to past frames
encoder_layer = torch.nn.TransformerEncoderLayer(
d_model=latent_dim,
nhead=8,
dim_feedforward=512,
batch_first=True
)
self.causal_transformer = torch.nn.TransformerEncoder(
encoder_layer, num_layers=4
)
# Score network: predicts ∇logp(x)self.score_head = torch.nn.Sequential(
torch.nn.Linear(latent_dim, 512),
torch.nn.ReLU(),
torch.nn.Linear(512, latent_dim)
)
defforward(self, latents, t=None):
"""
Predict score (gradient of log probability) with causal attention.
Args:
latents: (batch, time, latent_dim)
t: Optional diffusion timestep (not used for flows, but compatible)
Returns:
score: (batch, time, latent_dim) score predictions
"""# Create causal mask: each position only attends to itself and past
seq_len = latents.shape[1]
causal_mask = torch.triu(
torch.ones(seq_len, seq_len, device=latents.device) * float('-inf'),
diagonal=1
)
# Apply causal transformer
refined = self.causal_transformer(
latents, src_mask=causal_mask
)
# Predict score
score = self.score_head(refined)
return score
5. Training with Maximum Likelihood Estimation
Train flow model using exact likelihood through change-of-variables.
deftrain_normalizing_flow(
encoder,
flow_model,
video_batch,
optimizer,
learning_rate=1e-4):
"""
Single training step for STARFlow-V.
Optimizes exact likelihood using change-of-variables formula.
Args:
encoder: Invertible video encoder
flow_model: Normalizing flow
video_batch: (batch, time, channels, height, width) videos
optimizer: PyTorch optimizer
learning_rate: Gradient step size
Returns:
loss: Negative log-likelihood (for minimization)
"""# Encode video to latent space
latents, log_det_encoder = encoder(video_batch)
# Flatten for flow
batch_size = latents.shape[0]
latents_flat = latents.reshape(batch_size, -1)
# Forward through flow
z, log_det_flow = flow_model(latents_flat)
# Likelihood computation (change-of-variables)# log p(x) = log p(z) + log |det(dz/dx)|
log_p_z = -0.5 * (z ** 2).sum(dim=-1) # Standard normal log-prob
log_likelihood = log_p_z + log_det_flow + log_det_encoder
# Negative log-likelihood (for minimization)
nll_loss = -log_likelihood.mean()
# Backward and update
optimizer.zero_grad()
nll_loss.backward()
torch.nn.utils.clip_grad_norm_(
list(encoder.parameters()) + list(flow_model.parameters()),
1.0
)
optimizer.step()
return nll_loss.item()
6. Generation with Multiple Conditions
Use trained flow for flexible multi-task generation.
defgenerate_with_flow(
encoder,
flow_model,
condition_type='text',
condition_input=None,
num_frames=16,
device='cuda'):
"""
Generate video using trained flow model.
Supports text, image, or unconditioned generation.
Args:
encoder: Trained invertible encoder
flow_model: Trained normalizing flow
condition_type: 'text', 'image', or 'none'
condition_input: Condition (text string or image tensor)
num_frames: Number of frames to generate
device: Torch device
Returns:
generated_video: (1, num_frames, 3, height, width) video
"""# Sample from prior
latent_dim = flow_model.latent_dim
z = torch.randn(1, latent_dim, device=device)
# Decode through inverse flow
latents = flow_model.inverse(z)
# If conditioned, modulate latentsif condition_type == 'text':
# Encode text and modulate latents
text_embedding = encode_text(condition_input)
latents = latents + text_embedding
elif condition_type == 'image':
# Use image to guide latent generation
image_latent = encoder(condition_input.unsqueeze(1))
latents = 0.7 * latents + 0.3 * image_latent.mean(dim=1)
# Reshape latents
latents = latents.reshape(1, num_frames, -1, 8, 8) # Example spatial size# Decode to video
generated_video = encoder.inverse(latents)
return generated_video
Non-iterative sampling important (real-time applications)
Need for unified multi-task generation (text-to-video, image-to-video)
Applications where train-test mismatch is problematic
When NOT to Use:
Very high-resolution generation (>1080p) where flow computational cost dominates
Scenarios heavily optimized for diffusion models already
Tasks where diffusion's iterative refinement provides quality advantages
Key Hyperparameters:
num_flows: Number of invertible layers (8-32; more = better expressiveness)
coupling_layers_per_flow: Depth of coupling transformations (2-4)
global_compression_ratio: How much to compress temporal info (4-16×)
flow_score_mixing_weight: How much denoiser influences generation (0.1-0.3)
Performance Tips:
Pre-train encoder on large unlabeled video corpus before flow training
Use batch normalization cautiously (breaks invertibility); prefer layer norm
Cache encoder output to avoid redundant computation during flow training
For long videos, process in overlapping chunks and stitch results
Integration Pattern:
STARFlow-V naturally integrates into video diffusion pipelines as alternative backbone. Use flow for initial coarse generation, optionally refine with diffusion in high-detail region if needed.
