PaperlayerView exact revision on arXiv

Source-linked AI summary

Rolling Diffusion Models

David Ruhe, Jonathan Heek, Tim Salimans, Emiel Hoogeboom

arXiv:2402.09470v3cs.LGstat.ML

TL;DR

Temporal diffusion models often treat frames equally or lack a clear temporal inductive bias, despite the need to generate long sequences. Rolling Diffusion reparameterizes diffusion time per frame and denoises through a shifting local window, adding more noise to later frames. Across video and fluid-mechanics experiments, it outperforms existing methods when temporal dynamics are highly dynamic, subject to boundary-condition constraints.

  • Problem

    Temporal diffusion models face inefficient long-sequence generation, autoregressive error accumulation, and unclear parameterizations or temporal inductive biases.

  • Method

    Rolling Diffusion progressively noises data through time by assigning frame-specific local diffusion times and using a sliding-window denoising process.

  • Results

    Rolling Diffusion outperforms various existing methods when temporal dynamics are highly dynamic, across video and fluid-mechanics data.

  • Takeaways & Limitations

    The method’s temporal inductive bias is most effectively exploited for highly dynamic data, with potential applications in video, audio, and weather or climate modeling.

  • Takeaways & Limitations

    Boundary conditions can leave the initial sliding-window position containing partially denoised frames rather than a completely noisy state.

Abstract

from arXiv · show

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

1. Introduction

Rolling Diffusion addresses temporal-generation limitations by progressively increasing noise toward the future and denoising through a local sliding window. The framework is evaluated on video prediction and chaotic fluid mechanics.

  • Treating time as an extra spatial dimension can make long-sequence generation infeasible, while framewise autoregression is computationally intensive and accumulates errors.Block-autoregressive methods reduce some costs but typically apply the same denoising schedule to every frame.
  • Rolling Diffusion progressively corrupts data from past to future through a local sliding-window denoising process.It reparameterizes global diffusion time into frame-specific local times, creating a temporal inductive bias.
  • Frames farther from the conditioning receive more noise and therefore require only low-frequency predictions, while frames nearer the present receive finer high-frequency information.
  • Each frame is generated with preceding and succeeding frames, and the sliding-window formulation gives frames similar sampling procedures regardless of absolute video position.
  • The method’s merits are demonstrated in video prediction on Kinetics-600 and in chaotic fluid mechanics simulations.

2. Background: Diffusion Models

Diffusion models use stochastic noising followed by learned denoising, with a global time variable controlling the noise level. For temporal data, conditional extension raises parameterization and inductive-bias challenges beyond standard diffusion formulations.

  • A diffusion process gradually transforms data into noise, while a learned denoising process reconstructs samples by approximating the reverse distribution.The standard formulation uses a latent variable indexed by global diffusion time t, with x near z_0 and Gaussian noise near z_1.
  • The diffusion objective is expressed as a KL divergence between the forward diffusion and generative denoising processes, with weighting functions that can be freely specified.The supplied background notes that particular weightings, including ϵ-loss, can improve sample quality.
  • Rolling Diffusion assigns each frame a local diffusion time and applies a distinct signal-to-noise schedule, with later frames receiving more noise.The schedule preserves a monotonically decreasing signal-to-noise ratio while enforcing t_k ≤ t_{k+1}.
  • Temporal generation requires estimating conditional distributions for extending previously generated data, but optimal parameterizations and temporal inductive biases remain unclear.

3. Rolling Diffusion Models

Rolling Diffusion reparameterizes diffusion time per frame so later frames receive more noise, enabling local sliding-window denoising with temporal inductive biases. The framework supports position-independent sampling, indefinite rollout, and boundary-aware initialization.

  • 3.1. A global perspective: Rolling Diffusion reparameterizes global diffusion time into frame-dependent local times, assigning more noise to later frames as a temporal inductive bias.The local times are ordered so each frame is less denoised than the next earlier frame, reflecting progressively greater uncertainty toward the future.
  • 3.1. A global perspective: The generative process can focus on a local sliding window because frames outside the window are either already clean or independent noise.This factorization concentrates the nontrivial denoising computation on frames whose local noise levels change between diffusion steps.
  • 3.2. Local parameterization: A sliding-window schedule gives every frame the same inductive bias regardless of absolute video position and can be unfolded indefinitely at test time.The schedule is local and consistent when the window moves, so a frame’s denoising behavior is reused across positions.
  • 3.3. Boundary conditions: The linear local schedule creates boundary complications because the leftmost window position contains partially denoised frames rather than a fully noisy starting state.The standard rolling schedule is therefore supplemented with an initialization schedule that begins from maximum noise and reaches the rolling state.
  • 3.3. Boundary conditions: The model can be trained with an initialization schedule that handles boundaries, after which sampling resumes with the regular local schedule.This procedure starts from local times (1, 1, …, 1), denoises to the rolling state, and then continues with the linear schedule.

4. Related Work

Prior work applies diffusion to video and other temporal data, but often extends image models along time without autoregressive structure. Rolling Diffusion instead isolates local sliding-window effects and introduces schedules for boundary handling.

  • Video diffusion: Video diffusion commonly extends two-dimensional image models to a temporal dimension without autoregressive extension.
  • Autoregressive generation: Autoregressive video methods condition future-frame generation on past frames, whereas Rolling Diffusion explicitly introduces time into training.
  • Other time-series domains: Sequential diffusion has also been applied to audio, text, weather, and fluid mechanics, including denoising procedures for recovering high-frequency information in learned PDE emulators.
  • Rolling Diffusion: Rolling Diffusion isolates the sliding-window effect from auxiliary losses and adds schedules that handle boundaries for end-to-end sequence generation.

5. Experiments

Experiments compare Rolling Diffusion with standard diffusion across chaotic fluid forecasting and video prediction, including fixed-window and long autoregressive rollouts. Rolling Diffusion is competitive in simpler settings and is strongest when temporal dynamics are more variable or dynamic.

  • 5.1. Kolmogorov Flow: Rolling Diffusion consistently outperforms standard diffusion for chaotic fluid rollouts across conditioning settings and window sizes.The fluid task evaluates distributional fidelity with the Fréchet Spectral Distance rather than direct ground-truth RMSE.
  • 5.2. BAIR Robot Pushing Dataset: Both diffusion frameworks outperform previous BAIR Robot Pushing methods, with no significant difference between standard and rolling diffusion.The comparison uses one conditioning frame to predict the next 15 and evaluates samples with FVD.
  • 5.3. Kinetics-600: Standard diffusion achieves FVD 3.9 and Rolling Diffusion achieves a competitive FVD of 5.2 on the Kinetics-600 baseline task.This setting favors standard diffusion because it generates all frames at once and the short stride produces little dynamics.
  • 5.3. Kinetics-600: For Kinetics-600 autoregressive rollout, standard diffusion performs better at stride 1, whereas Rolling Diffusion consistently wins at the more dynamic stride 8 setting.The stride-8 experiment rolls out for 24 steps and predicts up to the 192th frame; single-frame diffusion underperforms and larger block autoregression is favorable.
  • 5.3. Kinetics-600: Slightly oversampling the linear rolling schedule produces the best result in the reported Kinetics-600 rollout setting.The oversampling rate is β = 0.9 in the stride-1 analysis, while the passage reports the best result for slight oversampling more generally.
  • 5.3. Kinetics-600: Across the experiments, Rolling Diffusion is particularly effective when the data is highly variable and the temporal dynamics are dynamic.The Kinetics-600 results distinguish more static short-stride sequences from longer, more dynamic rollouts.

6. Conclusion

Rolling Diffusion progressively noises and denoises data through time, with its inductive bias most effective for highly dynamic data. In that setting, it outperforms existing methods across video and fluid-mechanics evaluations.

  • Rolling Diffusion progressively noises and denoises data through time, and its inductive bias is most effective when the data is highly dynamic.
  • In highly dynamic settings, Rolling Diffusion outperforms various existing methods across video and fluid-mechanics data.
  • The framework motivates future applications in video, audio, and weather or climate modeling.

Impact Statement

Sequential generative models support detailed sampling in video generation and scientific research, but they also raise concerns about digital-media authenticity and originality. The supplied material additionally reviews diffusion objectives and rolling-diffusion optimization details.

  • Impact Statement: Sequential generative models enable fast, highly detailed sampling for applications including video generation and scientific research.
  • Impact Statement: These models can support more accurate and compelling synthesis in areas ranging from climate modeling to medical imaging.
  • Impact Statement: Their notable societal downsides concern the authenticity and originality of digital media content.

C. Hyperparameters

Experiments use U-ViT architectures, with larger models for BAIR and Kinetics-600 than for PDE experiments. Runtime comparisons fix model evaluations per frame, while the fluid setup varies physical parameters to introduce uncertainty.

  • C. Hyperparameters: Experiments use U-ViTs, with relatively small architectures for PDEs, larger models for BAIR, and the largest models for Kinetics-600.Kinetics-600 required larger architectures because it was the most difficult dataset.
  • D. Runtime Complexity: Runtime comparisons can fix 32 model evaluations per frame, allowing batch-autoregressive models to sample multiple frames jointly under the same budget.
  • D. Runtime Complexity: Rolling diffusion has slight training inefficiencies because partial noising reveals data and overlapping frames can let the model copy global structure.The authors suggest adjusting the noise schedule or fine-tuning standard diffusion with the rolling loss as possible remedies.
  • F.1. Kolmogorov Flow: Kolmogorov Flow uncertainty is introduced by varying viscosity and density, which must be inferred from the data.The resulting chaotic system is not deterministically predictable to arbitrary precision.

F.1. Kolmogorov Flow

For Kolmogorov Flow, MSE is best on MSE loss, whereas standard and especially Rolling Diffusion best match the frequency distribution according to FSD. Rolling Diffusion’s rollout intensity decreases farther from the conditioning frames under the MSE model.

  • F.1. Kolmogorov Flow: Standard diffusion and especially Rolling Diffusion are optimal for matching the frequency distribution by FSD, while the MSE model is optimal on MSE loss.Averaging Rolling Diffusion ensembles improves MSE but does not improve FSD.
  • F.1. Kolmogorov Flow: The reported Kolmogorov Flow results compare MSE and FSE errors at multiple time steps.
  • F.1. Kolmogorov Flow: In an example rollout, the MSE model’s intensity decreases farther from the conditioning frames.

F.2. Kinetics-600

The Kinetics-600 experiments compare Rolling Diffusion with TECO under long-horizon video generation settings and examine noise schedules and error growth during rollout. The evaluation uses 20 conditioning frames, generates 80 frames at 128 × 128 resolution, and includes FVD and MSE analyses.

  • Kinetics-600 comparison: 20 conditioning frames are used to generate 80 new 128 × 128 frames in the Kinetics-600 comparison with TECO (Yan et al., 2023).TECO uses 256 FVD samples in this setup.
  • Kinetics-600 comparison: FVD evaluation differs from other experiments because reference samples are matched on the conditioning frames under the low-sample-count TECO comparison.The table specifies 256 FVD samples for this comparison.
  • Error analysis: MSE relative to ground truth increases as generated frames move farther from the initial 20 conditioning frames, measured through rollouts to frame 80.Figure 8 uses the 20-12 setting at 128 × 128 resolution.
  • Noise schedules: The Kinetics-600 noise schedule samples from complete noise toward a rolling state before rollout generation, using a linear rolling sampling schedule.The schedule is described as not directly proportional to diffusion time t.
  • Noise schedules: The schedule design avoids redundant sampling in clean(s, t) associated with the clipped initialization schedule and provides the required local times at t = 1/W.The passages motivate the alternative schedule through the behavior of the clip operation.
  • Noise schedules: Table 10 compares oversampling with the linear rolling and initial noise schedules using 8192 FVD samples and 100 denoising steps per 11 frames.
Loading 2402.09470v3…