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One Frame, Full Heartbeat: ECG-Free Cardiac Cine MRI Synthesis via Phase-Conditioned Flow Matching

Shiyi Wang, Ruochen Sun, Peirong Liu, Xiang Li, Fangxu Xing

arXiv:2610.09397v1cs.CV

TL;DR

Cine CMR synthesis from a single frame is challenging because full-cycle functional assessment needs temporal information, while existing approaches may depend on ECG or lack physiological constraints. PhaseFlow uses nonlinear cardiac phase with phase-conditioned flow and deformation decoding; in an ablation, deformation decoding outperformed a standard VAE decoder on PSNR and FID.

  • Problem

    Synthesizing a physiologically coherent full-cycle CMR sequence from one frame is difficult because the frame lacks temporal information, while existing approaches may depend on ECG or lack physiological constraints.

    Source: §1 · p. 1

  • Method

    PhaseFlow estimates nonlinear phase from LV area and uses a phase-conditioned rectified-flow model with a diffeomorphic decoder that warps ED pixels directly.

    Source: §1 · p. 2

  • Results

    With deformation decoding, PSNR was 31.72 dB versus 27.28 dB and FID was 12.72 versus 89.63 for the standard VAE decoder ablation.

    Source: §4.3 · p. 6

  • Takeaways & Limitations

    The paper presents PhaseFlow as enabling physiologically grounded cine generation for retrospective cohorts, ECG-limited settings, and data augmentation for downstream tasks.

    Source: A Limitations and Broader Impact · p. 10

    Pathology-specific inference templates assume each pathology group has a characteristic phase trajectory distinct from others.

    Source: §3.2 · p. 3

Abstract

from arXiv · show

Cine cardiovascular magnetic resonance (CMR) analysis relies on multi-frame sequences capturing the full cardiac cycle. However, standard multi-frame acquisition depends heavily on electrocardiogram (ECG) gating and repeated breath-holds, posing challenges in uncooperative populations, resource-limited settings, and temporally corrupted datasets. Existing methods that synthesize full cardiac sequences either rely on explicit ECG signals to parameterize myocardium function, or employ deformable registration without physiological constraints, failing to faithfully reproduce clinically relevant dynamic metrics such as ejection fraction (EF) and ventricular contraction magnitude. We present PhaseFlow, a unified generative framework that overcomes both limitations. PhaseFlow estimates a non-linear cardiac phase signal directly from the input sequence via a segmentation-derived left-ventricular (LV) area curve, capturing the asymmetric dynamics of systole and diastole without any ECG dependency. At inference, this phase signal is provided by a pathology-specific template, informing phase-specific frame generation. A rectified flow model conditioned on the phase and slice position synthesizes the full cardiac motion trajectory in the latent space, decoded into a diffeomorphic displacement field that warps end-diastole pixel intensities directly, eliminating the reconstruction blur often accompanying the variational autoencoder. On the ACDC benchmark, PhaseFlow achieves superior physiological fidelity and image realism, with best LV volume curve $R^2$, structural similarity (SSIM) and generative quality (FID) among all baselines. Ablation studies confirm that each proposed component contributes measurably to the overall performance.

1 Introduction

PhaseFlow addresses the challenge of synthesizing a physiologically coherent cine CMR sequence from one frame without an explicit temporal signal. It estimates nonlinear cardiac phase from LV area and uses phase-conditioned flow matching and deformation decoding to generate the sequence.

1 Introduction

  • PhaseFlow targets full-cycle CMR synthesis from a single frame, a need arising when ECG-gated, multi-breath-hold acquisition is unavailable or only isolated frames survive.The task requires recovering myocardial motion over time from spatial information alone.Source: §1 · p. 1
  • Prior approaches either use linear frame indices that erase systole–diastole velocity asymmetry, depend on concurrent ECG, or lack physiological supervision for metrics such as EF and LV volumes.The cited discussion also notes domain-shift and near-static prediction concerns for some approaches.Source: §1 · p. 1
  • The paper identifies nonlinear cardiac phase, recoverable from the LV area curve without ECG, as a signal that captures asymmetric cardiac dynamics and varies systematically across pathologies.At inference, a pathology-specific template can supply phase when only one frame is available.Source: §1 · pp. 1–2
  • PhaseFlow combines ECG-free phase estimation with a rectified-flow generator conditioned on phase and slice position to synthesize the cardiac motion trajectory.The phase is derived from a segmentation-based LV area curve and represents each frame as [sin ϕt, cos ϕt].Source: §1 · p. 2
  • A deformation decoder turns predicted latent velocity into diffeomorphic displacements that warp ED pixels directly, while VolumeCurveLoss supervises the synthesized LV volume trajectory.Direct warping avoids the VAE decoding step; the loss uses a frozen segmentor on real CMR frames.Source: §1 · p. 2

2 Related Work

Prior cine-synthesis approaches use registration, generative models, or ECG conditioning, with limitations in phase representation, physiological supervision, or ECG independence. PhaseFlow instead repurposes diffeomorphic deformation as a generative decoder.

2 Related Work

  • Registration methods warp a reference frame but use frame index as a linear phase proxy, erasing systole–diastole velocity asymmetry and generalizing poorly across pathologies.The passage attributes the asymmetry concern to Yang et al. 2024.Source: §2 · p. 2
  • GAN and diffusion methods can achieve visual realism but lack physiological supervision for EF, while diffusion may require tens to hundreds of inference steps [Vukadinovic et al. 2023; Zhou et al. 2024; Phi et al. 2024; Algethami, Iqbal, and Ullah 2025].The passage states that these diffusion-step requirements preclude real-time clinical deployment.Source: §2 · p. 2
  • ECG-conditioned methods restore temporal coherence but require concurrent ECG acquisition, limiting use with retrospective or resource-limited datasets [Fang et al. 2026].Source: §2 · p. 2
  • Unlike registration systems that estimate displacement between observed images, PhaseFlow generates displacement from latent velocity as a decoder while maintaining anatomical plausibility.The passage describes scaling-and-squaring as a computationally efficient route to diffeomorphic transformations.Source: §2 · p. 2

3 Methods

PhaseFlow synthesizes a cine sequence from an ED frame using nonlinear cardiac phase as an external temporal signal. Its method combines phase-conditioned latent flow, diffeomorphic pixel warping, and objectives for image similarity, deformation smoothness, and LV-volume trajectory.

3 Methods

  • PhaseFlow encodes an ED frame, conditions rectified flow on cardiac phase and slice position, and decodes latent velocity into a diffeomorphic field that warps ED intensities into a cine sequence.Source: §3 · p. 2, Figure 1 · p. 3

3.1 Problem Formulation

  • The single-frame synthesis task is ill-posed because functional assessment requires complete temporal sequences, so the method uses nonlinear cardiac phase as an external temporal signal.Source: §3.1 · p. 2

3.2 ECG-Free Nonlinear Phase Estimation

  • Nonlinear phase accumulates according to myocardial displacement rather than frame index, aligning end-systole near ϕ ≈ π across patients regardless of heart rate or pathology.At inference, a mean phase template for the relevant pathology group supplies the schedule; this assumes groups have characteristic phase trajectories.Source: §3.2 · p. 3, Figure 2 · p. 3

3.3 Phase-Conditioned Latent Flow Matching

  • Rectified flow transports the ED anchor latent toward the full-sequence latent along a straight path, with a 3D UNet predicting velocity conditioned on flow time, phase, and slice position.At inference, the model queries the velocity network at τ = 1 without iterative ODE integration.Source: §3.3 · pp. 3–4

3.4 Deformation-Decoded Pixel Synthesis

  • A deformation decoder maps latent velocity to an image-space field that is integrated into diffeomorphic displacements and used to warp the original ED frame, avoiding VAE reconstruction blur.The method states that the deformation has positive spatial Jacobian determinant at every pixel.Source: §3.4 · p. 4

3.5 Training Objectives

  • Training combines latent flow matching with image-space similarity, bending-energy regularization, and VolumeCurveLoss for LV-volume trajectory supervision.The frozen segmentor processes real frames only, avoiding domain shift from applying it to generated images and keeping gradients reliable.Source: §3.5 · pp. 4–5

4 Experiments and Results

PhaseFlow was evaluated for image quality and physiological fidelity on ACDC, with ablations and zero-shot testing on M&Ms. Results and visual comparisons cover baseline performance, component contributions, cross-dataset transfer, and synthesized motion quality.

4.1 Experiment Setup

  • ACDC evaluation used 150 subjects from five pathology groups in a stratified 105/15/30 train-validation-test split; it assessed PSNR, SSIM, LPIPS, FID, EF MAE, Vol Corr, Vol R2 and Vol MAE.Five baselines were retrained on the same ACDC split under identical conditions.Source: §4.1 · p. 5

4.2 Comparison to Baselines

  • Vol R2 (0.363) was the only positive score; PhaseFlow also achieved the best SSIM (0.956) and FID (12.72) among baselines.EchoDiff had the lowest EF MAE (15.47%) but SSIM 0.219, FID 115.17, and Vol R2 −1.00.Source: §4.2 · p. 5, Table 1 · p. 6

4.3 Ablation Study

  • VAE decoding reduced PSNR to 27.28 dB and raised FID to 89.63, while removing LNCC dropped PSNR to 15.17 dB and SSIM to 0.238.The VAE ablation also reduced Vol R2 from 0.363 to −0.548; without LNCC, physiological metrics remained reasonable despite visually unusable images.Source: Table 2 · p. 6, §4.3 · p. 6
  • Linear phase worsened EF MAE (21.30% vs. 17.79%) and Vol R2 (0.069 vs. 0.363), while removing volume loss raised EF MAE to 26.80% and lowered Vol R2 to 0.071.Nonlinear phase was particularly beneficial for pathologies with pronounced systole–diastole asymmetry; removing volume loss preserved image quality (PSNR 31.76 dB).Source: Table 2 · p. 6, §4.3 · p. 6

4.4 Zero-Shot Cross-Dataset Generalization

  • Without fine-tuning, ACDC-trained PhaseFlow transferred to 136 M&Ms patients across 1,621 slices; image quality improved while physiological fidelity stayed close to in-domain levels.Inference used ACDC pathology-specific phase templates, which did not perfectly represent M&Ms acquisition dynamics.Source: Table 3 · p. 6, §4.4 · p. 6

4.5 Qualitative Results

  • Predicted LV volume curves reproduced pathology-specific contraction patterns and aligned temporally with ground truth, including asymmetric systole–diastole velocity profiles.Qualitative examples show sharp, anatomically coherent frames and smooth myocardial deformation; PhaseFlow-VAE exhibits blur, especially at fine anatomical boundaries.Source: Figure 3 · p. 7, §4.5 · p. 7, Figure 4 · p. 7

5 Conclusion

PhaseFlow synthesizes a physiologically faithful cardiac cine MRI sequence from a single end-diastolic frame without ECG dependency. A nonlinear phase and flow-matching generator support the approach, which showed strong physiological fidelity and image realism on ACDC and zero-shot transfer across sites and vendors.

5 Conclusion

  • PhaseFlow conditions a flow-matching generator on nonlinear cardiac phase supplied by a pathology-specific template, then uses a diffeomorphic decoder to synthesize a coherent motion trajectory from one end-diastolic frame without ECG.Experiments on ACDC and zero-shot evaluation across scanner vendors and clinical sites demonstrated superior physiological fidelity and image realism.Source: §5 · p. 7

A Limitations and Broader Impact

The authors identify boundaries on clinical readiness and scope, alongside potential applications in settings without ECG-gated infrastructure.

A Limitations and Broader Impact

  • EF MAE remains 17.79%, above the approximately 10% clinical diagnostic threshold, and larger, more diverse cine CMR cohorts are needed before clinical deployment.Phase estimation relies on SegUNet LV segmentation, so low image quality or heavy motion artifacts may degrade the phase signal and synthesized physiological fidelity.Source: A Limitations and Broader Impact · p. 10
  • The authors identify retrospective cohort studies, resource-limited settings without ECG-gated infrastructure, and downstream segmentation and disease classification augmentation as potential applications.The current evaluation is limited to CMR; extension to echocardiography and lung MRI remains future work.Source: A Limitations and Broader Impact · p. 10

B Nonlinear Phase Templates: Empirical Analysis

Pathology-level nonlinear phase templates preserve a fast systolic and slower diastolic progression, and better approximate individual phase curves than a linear baseline. The deformation verification reports no folding across generated frames and pathology groups.

B.1 Phase Template Visualization

  • The group-mean template is computed by averaging nonlinear phase curves from training subjects within each ACDC pathology group.Figure 5 compares these per-group means with a uniform linear phase baseline.Source: §B.1 · p. 10
  • All five pathology groups show rapid systolic phase accumulation followed by slower diastolic progression, unlike the constant-rate linear baseline.NOR progresses earlier; DCM and MINF show delayed acceleration.Source: §B.1 · p. 10, Figure 5 · p. 10

B.2 Intra-Group Consistency

  • The group-mean template’s RMSE equals intra-group standard deviation by construction, while linear phase adds systematic bias.The passage expresses this relationship as RMSElin = √(bias² + σ²) ≥ RMSEnl.Source: §B.2 · p. 10
  • 7.3–9.7% of the cardiac cycle was the nonlinear-template mean RMSE, versus 8.3–13.7% for linear phase, with up to 1.7× lower error.The largest reduction was in the NOR group.Source: §B.2 · p. 10

C Diffeomorphism Verification

  • The deformation decoder integrates a 2-D velocity field with K = 7 scaling-and-squaring steps to produce φ = exp(u).The verification tests the claim that this integration yields a fold-free, topology-preserving deformation.Source: C Diffeomorphism Verification · p. 10
  • The study computes det(Jφ) by central finite differences at every pixel in every generated frame across test slices, with 30 frames per slice.A nonpositive determinant marks a folding pixel.Source: C Diffeomorphism Verification · p. 10
  • 0.00% of pixels had det(Jφ) ≤ 0, and the mean determinant was 1.001 ± 0.063 across generated frames.The authors report consistent per-pathology statistics.Source: C Diffeomorphism Verification · p. 10

D Excluded Baselines

Several baselines were excluded because they could not support the study’s evaluation setting or lacked an available implementation. The supplied figures also report phase-template error reduction and deformation fold checks.

Phase-template comparison

  • The nonlinear group template reduced per-frame phase approximation error by up to 1.7× versus the linear baseline.Figure 6 depicts the phase RMSE curves and the error gap.Source: Figure 6 · p. 11

Deformation verification

  • The det(Jφ) distribution showed zero folding across pixels for the reported scaling-and-squaring configuration.Figure 7 presents a global histogram and per-pathology mean ± standard deviation.Source: Figure 7 · p. 11

Excluded baselines

  • 19 of 30 test cases (63%) failed frozen SegUNet evaluation after DragNet’s autoregressive prediction drift, making physiological volume-curve evaluation infeasible.The passage attributes the drift to accumulating prediction error over the sequence.Source: D Excluded Baselines · p. 11
  • Registration methods cannot synthesize a sequence from one ED frame when no target frame is available at inference.The passage distinguishes registration’s task of aligning two observed images.Source: D Excluded Baselines · p. 11
  • ECG-conditioned methods were excluded because concurrent ECG acquisition violates the ECG-free setting and makes direct comparison unfair.Source: D Excluded Baselines · p. 11
  • EchoLVFM had no publicly available implementation, preventing its inclusion in the direct comparison.Source: D Excluded Baselines · p. 11

E Implementation Details

The implementation combines a frozen 3D VAE, phase-conditioned latent flow model, and deformation decoder, with preprocessing and evaluation procedures specified for ACDC data. Evaluation covers image similarity and LV physiological fidelity.

E Implementation Details

  • The VAE preserves temporal resolution while compressing spatial dimensions 8×, and its latent shape is (B, 4, T, 16, 16) for input (B, 1, T, 128, 128).The VAE is pretrained for 100 epochs and frozen during flow-matching training.Source: E Implementation Details · p. 11
  • The VelocityUNet uses temporal self-attention and injects phase embeddings through cross-attention, while slice position and flow time condition adaptive group normalization.The deformation decoder upsamples the latent prediction to a two-channel velocity field and uses K = 7 scaling-and-squaring steps.Source: E Implementation Details · p. 11
  • SegUNet is trained on ACDC LV, RV, and myocardium annotations, then frozen for phase estimation, VolumeCurveLoss, and volume-curve evaluation.It is never exposed to generated images during training.Source: E Implementation Details · p. 11

F Data Preprocessing

  • The ACDC preprocessing stratifies 150 patients into train/validation/test sets of 105/15/30 and caches segmentation-derived nonlinear phase curves.Per-slice sequences are normalized to [−1, 1], resized to 128 × 128, resampled to 30 frames, and paired with the ED anchor and slice position.Source: F Data Preprocessing · p. 12
  • Preprocessing applies no intensity augmentation, cropping, or registration; one per-sequence intensity range preserves relative temporal contrast across frames.The split and phase cache are reused across models for an identical evaluation protocol.Source: F Data Preprocessing · p. 12

G Evaluation Metrics

  • Image evaluation includes PSNR, SSIM, LPIPS, and FID, while physiological evaluation includes EF MAE, Vol Corr, Vol R2, and normalized Vol MAE.Predicted LV volumes come from warping the ED segmentation mask through the predicted displacement field, avoiding generated-frame segmentation domain shift.Source: G Evaluation Metrics · p. 12
  • EF MAE measures ejection-fraction error, Vol Corr measures volume-curve shape, Vol R2 penalizes bias and variance, and Vol MAE is normalized by ED volume.Physiological metrics are computed on warped ED masks rather than segmentations of generated frames.Source: G Evaluation Metrics · p. 12

H Statistical Analysis

PhaseFlow’s volume-curve R2 is significantly better than every tested baseline, while its physiological metrics vary more across patients than its image-quality metrics. The analysis reports paired tests and per-case variability on the ACDC test set.

Metric variability

  • 0.363 ± 0.489 was PhaseFlow’s test-set Vol R2, compared with SSIM of 0.956 ± 0.019 across the reported cases.Image-quality metrics are per-slice (n=298), while physiological metrics are per-patient (n=30); all values come from one fixed-seed training run.Source: H Statistical Analysis · p. 13, Table 4 · p. 13

Statistical comparisons

  • The paired Wilcoxon signed-rank tests compare per-patient physiological metrics against ED Repeat, ConvLSTM, CVAE, and Direct Registration.The reported cells are p-values, with bold entries significant at α = 0.05.Source: H Statistical Analysis · p. 13, Table 5 · p. 13
  • PhaseFlow was also significantly better on Vol MAE and EF MAE against all baselines except Direct Registration.For Vol Corr, it was statistically indistinguishable from CVAE and Direct Registration (p = 0.36 and 0.72); those methods had negative R2.Source: H Statistical Analysis · p. 13
  • p = 1.6×10−2 to 1.9×10−9 for Vol R2 comparisons, with PhaseFlow significantly better than every baseline in the paired Wilcoxon tests.Table 5 reports p-values for 30 patients; Vol Corr versus ED Repeat is undefined because its volume curve is constant.Source: Table 5 · p. 13, H Statistical Analysis · p. 13

I Latent Scale and Anchor Perturbation

The anchor perturbation is large by norm but has little projection onto the transport direction, supporting α=0.1 as a safe choice. Latent statistics agree across ACDC splits.

Latent scale

Geometry of the perturbation

  • The anchor perturbation is effectively harmless to motion content, making α=0.1 a safe choice.The analysis attributes this to noise being almost entirely orthogonal to the motion direction.Source: I Latent Scale and Anchor Perturbation · p. 13
  • 0.284% of the transport distance is the noise projection onto the transport direction, despite the noise norm being 66% of the transport distance.The projection is 0.074 ± 0.089, while the transport distance is 29.33 ± 8.51 and the noise norm is 17.54 ± 0.07.Source: I Latent Scale and Anchor Perturbation · p. 13
  • The perturbed and clean transport directions differ by 32.5° ± 8.3°, while the component that corrupts the motion signal is described as negligible.The noise samples a wide cone of starting points around the anchor, but the paths terminate at the same z1.Source: I Latent Scale and Anchor Perturbation · p. 14

J Extended Qualitative Results

The extended qualitative results show representative PhaseFlow syntheses for each ACDC pathology group, using only the ED frame as input. The generated sequences capture the characteristic motion signatures described for the groups.

Extended qualitative results

  • Figure 8 shows one manually selected representative patient per pathology group, with ground truth above PhaseFlow synthesis.Each group is shown at six evenly spaced frames spanning the full cardiac cycle.Source: J Extended Qualitative Results · p. 14, Figure 8 · p. 14
  • The ED frame at t = 0 is the sole model input; subsequent frames are synthesized from the nonlinear phase template and predicted diffeomorphic displacement field.The ED frame is the leftmost frame in the figure.Source: J Extended Qualitative Results · p. 14, Figure 8 · p. 14
  • PhaseFlow captures characteristic motion signatures across NOR, DCM, HCM, MINF, and ARV.These are normal wall-thickening, large-cavity contraction, asymmetric septal hypertrophy, regional wall-motion abnormality, and preserved right ventricular dynamics, respectively.Source: J Extended Qualitative Results · p. 14

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