diff --git a/README.md b/README.md
index df33148..48145a1 100644
--- a/README.md
+++ b/README.md
@@ -101,6 +101,37 @@ Then, in the same directory
 $ accelerate launch train.py
 ```
 
+## Miscellaenous
+
+By popular request, a 1D Unet + Gaussian Diffusion implementation. You will have to do the training code yourself
+
+```python
+import torch
+from denoising_diffusion_pytorch import Unet1D, GaussianDiffusion1D
+
+model = Unet1D(
+    dim = 64,
+    dim_mults = (1, 2, 4, 8),
+    channels = 32
+)
+
+diffusion = GaussianDiffusion1D(
+    model,
+    seq_length = 128,
+    timesteps = 1000,
+    objective = 'pred_v'
+)
+
+training_seq = torch.randn(8, 32, 128) # features are normalized from 0 to 1
+loss = diffusion(training_seq)
+loss.backward()
+
+# after a lot of training
+
+sampled_seq = diffusion.sample(batch_size = 4)
+sampled_seq.shape # (4, 32, 128)
+```
+
 ## Citations
 
 ```bibtex
diff --git a/denoising_diffusion_pytorch/__init__.py b/denoising_diffusion_pytorch/__init__.py
index 5382b46..ab5108d 100644
--- a/denoising_diffusion_pytorch/__init__.py
+++ b/denoising_diffusion_pytorch/__init__.py
@@ -5,3 +5,6 @@ from denoising_diffusion_pytorch.continuous_time_gaussian_diffusion import Conti
 from denoising_diffusion_pytorch.weighted_objective_gaussian_diffusion import WeightedObjectiveGaussianDiffusion
 from denoising_diffusion_pytorch.elucidated_diffusion import ElucidatedDiffusion
 from denoising_diffusion_pytorch.v_param_continuous_time_gaussian_diffusion import VParamContinuousTimeGaussianDiffusion
+
+from denoising_diffusion_pytorch.denoising_diffusion_pytorch_1d import GaussianDiffusion1D, Unet1D
+
diff --git a/denoising_diffusion_pytorch/denoising_diffusion_pytorch_1d.py b/denoising_diffusion_pytorch/denoising_diffusion_pytorch_1d.py
new file mode 100644
index 0000000..327f34f
--- /dev/null
+++ b/denoising_diffusion_pytorch/denoising_diffusion_pytorch_1d.py
@@ -0,0 +1,695 @@
+import math
+from random import random
+from functools import partial
+from collections import namedtuple
+
+import torch
+from torch import nn, einsum
+import torch.nn.functional as F
+
+from einops import rearrange, reduce
+from einops.layers.torch import Rearrange
+
+from tqdm.auto import tqdm
+
+# constants
+
+ModelPrediction =  namedtuple('ModelPrediction', ['pred_noise', 'pred_x_start'])
+
+# helpers functions
+
+def exists(x):
+    return x is not None
+
+def default(val, d):
+    if exists(val):
+        return val
+    return d() if callable(d) else d
+
+def identity(t, *args, **kwargs):
+    return t
+
+def cycle(dl):
+    while True:
+        for data in dl:
+            yield data
+
+def has_int_squareroot(num):
+    return (math.sqrt(num) ** 2) == num
+
+def num_to_groups(num, divisor):
+    groups = num // divisor
+    remainder = num % divisor
+    arr = [divisor] * groups
+    if remainder > 0:
+        arr.append(remainder)
+    return arr
+
+def convert_image_to_fn(img_type, image):
+    if image.mode != img_type:
+        return image.convert(img_type)
+    return image
+
+# normalization functions
+
+def normalize_to_neg_one_to_one(img):
+    return img * 2 - 1
+
+def unnormalize_to_zero_to_one(t):
+    return (t + 1) * 0.5
+
+# small helper modules
+
+class Residual(nn.Module):
+    def __init__(self, fn):
+        super().__init__()
+        self.fn = fn
+
+    def forward(self, x, *args, **kwargs):
+        return self.fn(x, *args, **kwargs) + x
+
+def Upsample(dim, dim_out = None):
+    return nn.Sequential(
+        nn.Upsample(scale_factor = 2, mode = 'nearest'),
+        nn.Conv1d(dim, default(dim_out, dim), 3, padding = 1)
+    )
+
+def Downsample(dim, dim_out = None):
+    return nn.Conv1d(dim, default(dim_out, dim), 4, 2, 1)
+
+class WeightStandardizedConv2d(nn.Conv1d):
+    """
+    https://arxiv.org/abs/1903.10520
+    weight standardization purportedly works synergistically with group normalization
+    """
+    def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
+
+        weight = self.weight
+        mean = reduce(weight, 'o ... -> o 1 1', 'mean')
+        var = reduce(weight, 'o ... -> o 1 1', partial(torch.var, unbiased = False))
+        normalized_weight = (weight - mean) * (var + eps).rsqrt()
+
+        return F.conv1d(x, normalized_weight, self.bias, self.stride, self.padding, self.dilation, self.groups)
+
+class LayerNorm(nn.Module):
+    def __init__(self, dim):
+        super().__init__()
+        self.g = nn.Parameter(torch.ones(1, dim, 1))
+
+    def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
+        var = torch.var(x, dim = 1, unbiased = False, keepdim = True)
+        mean = torch.mean(x, dim = 1, keepdim = True)
+        return (x - mean) * (var + eps).rsqrt() * self.g
+
+class PreNorm(nn.Module):
+    def __init__(self, dim, fn):
+        super().__init__()
+        self.fn = fn
+        self.norm = LayerNorm(dim)
+
+    def forward(self, x):
+        x = self.norm(x)
+        return self.fn(x)
+
+# sinusoidal positional embeds
+
+class SinusoidalPosEmb(nn.Module):
+    def __init__(self, dim):
+        super().__init__()
+        self.dim = dim
+
+    def forward(self, x):
+        device = x.device
+        half_dim = self.dim // 2
+        emb = math.log(10000) / (half_dim - 1)
+        emb = torch.exp(torch.arange(half_dim, device=device) * -emb)
+        emb = x[:, None] * emb[None, :]
+        emb = torch.cat((emb.sin(), emb.cos()), dim=-1)
+        return emb
+
+class RandomOrLearnedSinusoidalPosEmb(nn.Module):
+    """ following @crowsonkb 's lead with random (learned optional) sinusoidal pos emb """
+    """ https://github.com/crowsonkb/v-diffusion-jax/blob/master/diffusion/models/danbooru_128.py#L8 """
+
+    def __init__(self, dim, is_random = False):
+        super().__init__()
+        assert (dim % 2) == 0
+        half_dim = dim // 2
+        self.weights = nn.Parameter(torch.randn(half_dim), requires_grad = not is_random)
+
+    def forward(self, x):
+        x = rearrange(x, 'b -> b 1')
+        freqs = x * rearrange(self.weights, 'd -> 1 d') * 2 * math.pi
+        fouriered = torch.cat((freqs.sin(), freqs.cos()), dim = -1)
+        fouriered = torch.cat((x, fouriered), dim = -1)
+        return fouriered
+
+# building block modules
+
+class Block(nn.Module):
+    def __init__(self, dim, dim_out, groups = 8):
+        super().__init__()
+        self.proj = WeightStandardizedConv2d(dim, dim_out, 3, padding = 1)
+        self.norm = nn.GroupNorm(groups, dim_out)
+        self.act = nn.SiLU()
+
+    def forward(self, x, scale_shift = None):
+        x = self.proj(x)
+        x = self.norm(x)
+
+        if exists(scale_shift):
+            scale, shift = scale_shift
+            x = x * (scale + 1) + shift
+
+        x = self.act(x)
+        return x
+
+class ResnetBlock(nn.Module):
+    def __init__(self, dim, dim_out, *, time_emb_dim = None, groups = 8):
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.SiLU(),
+            nn.Linear(time_emb_dim, dim_out * 2)
+        ) if exists(time_emb_dim) else None
+
+        self.block1 = Block(dim, dim_out, groups = groups)
+        self.block2 = Block(dim_out, dim_out, groups = groups)
+        self.res_conv = nn.Conv1d(dim, dim_out, 1) if dim != dim_out else nn.Identity()
+
+    def forward(self, x, time_emb = None):
+
+        scale_shift = None
+        if exists(self.mlp) and exists(time_emb):
+            time_emb = self.mlp(time_emb)
+            time_emb = rearrange(time_emb, 'b c -> b c 1')
+            scale_shift = time_emb.chunk(2, dim = 1)
+
+        h = self.block1(x, scale_shift = scale_shift)
+
+        h = self.block2(h)
+
+        return h + self.res_conv(x)
+
+class LinearAttention(nn.Module):
+    def __init__(self, dim, heads = 4, dim_head = 32):
+        super().__init__()
+        self.scale = dim_head ** -0.5
+        self.heads = heads
+        hidden_dim = dim_head * heads
+        self.to_qkv = nn.Conv1d(dim, hidden_dim * 3, 1, bias = False)
+
+        self.to_out = nn.Sequential(
+            nn.Conv1d(hidden_dim, dim, 1),
+            LayerNorm(dim)
+        )
+
+    def forward(self, x):
+        b, c, n = x.shape
+        qkv = self.to_qkv(x).chunk(3, dim = 1)
+        q, k, v = map(lambda t: rearrange(t, 'b (h c) n -> b h c n', h = self.heads), qkv)
+
+        q = q.softmax(dim = -2)
+        k = k.softmax(dim = -1)
+
+        q = q * self.scale        
+
+        context = torch.einsum('b h d n, b h e n -> b h d e', k, v)
+
+        out = torch.einsum('b h d e, b h d n -> b h e n', context, q)
+        out = rearrange(out, 'b h c n -> b (h c) n', h = self.heads)
+        return self.to_out(out)
+
+class Attention(nn.Module):
+    def __init__(self, dim, heads = 4, dim_head = 32):
+        super().__init__()
+        self.scale = dim_head ** -0.5
+        self.heads = heads
+        hidden_dim = dim_head * heads
+
+        self.to_qkv = nn.Conv1d(dim, hidden_dim * 3, 1, bias = False)
+        self.to_out = nn.Conv1d(hidden_dim, dim, 1)
+
+    def forward(self, x):
+        b, c, n = x.shape
+        qkv = self.to_qkv(x).chunk(3, dim = 1)
+        q, k, v = map(lambda t: rearrange(t, 'b (h c) n -> b h c n', h = self.heads), qkv)
+
+        q = q * self.scale
+
+        sim = einsum('b h d i, b h d j -> b h i j', q, k)
+        attn = sim.softmax(dim = -1)
+        out = einsum('b h i j, b h d j -> b h i d', attn, v)
+
+        out = rearrange(out, 'b h n d -> b (h d) n')
+        return self.to_out(out)
+
+# model
+
+class Unet1D(nn.Module):
+    def __init__(
+        self,
+        dim,
+        init_dim = None,
+        out_dim = None,
+        dim_mults=(1, 2, 4, 8),
+        channels = 3,
+        self_condition = False,
+        resnet_block_groups = 8,
+        learned_variance = False,
+        learned_sinusoidal_cond = False,
+        random_fourier_features = False,
+        learned_sinusoidal_dim = 16
+    ):
+        super().__init__()
+
+        # determine dimensions
+
+        self.channels = channels
+        self.self_condition = self_condition
+        input_channels = channels * (2 if self_condition else 1)
+
+        init_dim = default(init_dim, dim)
+        self.init_conv = nn.Conv1d(input_channels, init_dim, 7, padding = 3)
+
+        dims = [init_dim, *map(lambda m: dim * m, dim_mults)]
+        in_out = list(zip(dims[:-1], dims[1:]))
+
+        block_klass = partial(ResnetBlock, groups = resnet_block_groups)
+
+        # time embeddings
+
+        time_dim = dim * 4
+
+        self.random_or_learned_sinusoidal_cond = learned_sinusoidal_cond or random_fourier_features
+
+        if self.random_or_learned_sinusoidal_cond:
+            sinu_pos_emb = RandomOrLearnedSinusoidalPosEmb(learned_sinusoidal_dim, random_fourier_features)
+            fourier_dim = learned_sinusoidal_dim + 1
+        else:
+            sinu_pos_emb = SinusoidalPosEmb(dim)
+            fourier_dim = dim
+
+        self.time_mlp = nn.Sequential(
+            sinu_pos_emb,
+            nn.Linear(fourier_dim, time_dim),
+            nn.GELU(),
+            nn.Linear(time_dim, time_dim)
+        )
+
+        # layers
+
+        self.downs = nn.ModuleList([])
+        self.ups = nn.ModuleList([])
+        num_resolutions = len(in_out)
+
+        for ind, (dim_in, dim_out) in enumerate(in_out):
+            is_last = ind >= (num_resolutions - 1)
+
+            self.downs.append(nn.ModuleList([
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim),
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim),
+                Residual(PreNorm(dim_in, LinearAttention(dim_in))),
+                Downsample(dim_in, dim_out) if not is_last else nn.Conv1d(dim_in, dim_out, 3, padding = 1)
+            ]))
+
+        mid_dim = dims[-1]
+        self.mid_block1 = block_klass(mid_dim, mid_dim, time_emb_dim = time_dim)
+        self.mid_attn = Residual(PreNorm(mid_dim, Attention(mid_dim)))
+        self.mid_block2 = block_klass(mid_dim, mid_dim, time_emb_dim = time_dim)
+
+        for ind, (dim_in, dim_out) in enumerate(reversed(in_out)):
+            is_last = ind == (len(in_out) - 1)
+
+            self.ups.append(nn.ModuleList([
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim),
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim),
+                Residual(PreNorm(dim_out, LinearAttention(dim_out))),
+                Upsample(dim_out, dim_in) if not is_last else  nn.Conv1d(dim_out, dim_in, 3, padding = 1)
+            ]))
+
+        default_out_dim = channels * (1 if not learned_variance else 2)
+        self.out_dim = default(out_dim, default_out_dim)
+
+        self.final_res_block = block_klass(dim * 2, dim, time_emb_dim = time_dim)
+        self.final_conv = nn.Conv1d(dim, self.out_dim, 1)
+
+    def forward(self, x, time, x_self_cond = None):
+        if self.self_condition:
+            x_self_cond = default(x_self_cond, lambda: torch.zeros_like(x))
+            x = torch.cat((x_self_cond, x), dim = 1)
+
+        x = self.init_conv(x)
+        r = x.clone()
+
+        t = self.time_mlp(time)
+
+        h = []
+
+        for block1, block2, attn, downsample in self.downs:
+            x = block1(x, t)
+            h.append(x)
+
+            x = block2(x, t)
+            x = attn(x)
+            h.append(x)
+
+            x = downsample(x)
+
+        x = self.mid_block1(x, t)
+        x = self.mid_attn(x)
+        x = self.mid_block2(x, t)
+
+        for block1, block2, attn, upsample in self.ups:
+            x = torch.cat((x, h.pop()), dim = 1)
+            x = block1(x, t)
+
+            x = torch.cat((x, h.pop()), dim = 1)
+            x = block2(x, t)
+            x = attn(x)
+
+            x = upsample(x)
+
+        x = torch.cat((x, r), dim = 1)
+
+        x = self.final_res_block(x, t)
+        return self.final_conv(x)
+
+# gaussian diffusion trainer class
+
+def extract(a, t, x_shape):
+    b, *_ = t.shape
+    out = a.gather(-1, t)
+    return out.reshape(b, *((1,) * (len(x_shape) - 1)))
+
+def linear_beta_schedule(timesteps):
+    scale = 1000 / timesteps
+    beta_start = scale * 0.0001
+    beta_end = scale * 0.02
+    return torch.linspace(beta_start, beta_end, timesteps, dtype = torch.float64)
+
+def cosine_beta_schedule(timesteps, s = 0.008):
+    """
+    cosine schedule
+    as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
+    """
+    steps = timesteps + 1
+    x = torch.linspace(0, timesteps, steps, dtype = torch.float64)
+    alphas_cumprod = torch.cos(((x / timesteps) + s) / (1 + s) * math.pi * 0.5) ** 2
+    alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
+    betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
+    return torch.clip(betas, 0, 0.999)
+
+class GaussianDiffusion1D(nn.Module):
+    def __init__(
+        self,
+        model,
+        *,
+        seq_length,
+        timesteps = 1000,
+        sampling_timesteps = None,
+        loss_type = 'l1',
+        objective = 'pred_noise',
+        beta_schedule = 'cosine',
+        p2_loss_weight_gamma = 0.,
+        p2_loss_weight_k = 1,
+        ddim_sampling_eta = 1.
+    ):
+        super().__init__()
+        self.model = model
+        self.channels = self.model.channels
+        self.self_condition = self.model.self_condition
+
+        self.seq_length = seq_length
+
+        self.objective = objective
+
+        assert objective in {'pred_noise', 'pred_x0', 'pred_v'}, 'objective must be either pred_noise (predict noise) or pred_x0 (predict image start) or pred_v (predict v [v-parameterization as defined in appendix D of progressive distillation paper, used in imagen-video successfully])'
+
+        if beta_schedule == 'linear':
+            betas = linear_beta_schedule(timesteps)
+        elif beta_schedule == 'cosine':
+            betas = cosine_beta_schedule(timesteps)
+        else:
+            raise ValueError(f'unknown beta schedule {beta_schedule}')
+
+        alphas = 1. - betas
+        alphas_cumprod = torch.cumprod(alphas, dim=0)
+        alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value = 1.)
+
+        timesteps, = betas.shape
+        self.num_timesteps = int(timesteps)
+        self.loss_type = loss_type
+
+        # sampling related parameters
+
+        self.sampling_timesteps = default(sampling_timesteps, timesteps) # default num sampling timesteps to number of timesteps at training
+
+        assert self.sampling_timesteps <= timesteps
+        self.is_ddim_sampling = self.sampling_timesteps < timesteps
+        self.ddim_sampling_eta = ddim_sampling_eta
+
+        # helper function to register buffer from float64 to float32
+
+        register_buffer = lambda name, val: self.register_buffer(name, val.to(torch.float32))
+
+        register_buffer('betas', betas)
+        register_buffer('alphas_cumprod', alphas_cumprod)
+        register_buffer('alphas_cumprod_prev', alphas_cumprod_prev)
+
+        # calculations for diffusion q(x_t | x_{t-1}) and others
+
+        register_buffer('sqrt_alphas_cumprod', torch.sqrt(alphas_cumprod))
+        register_buffer('sqrt_one_minus_alphas_cumprod', torch.sqrt(1. - alphas_cumprod))
+        register_buffer('log_one_minus_alphas_cumprod', torch.log(1. - alphas_cumprod))
+        register_buffer('sqrt_recip_alphas_cumprod', torch.sqrt(1. / alphas_cumprod))
+        register_buffer('sqrt_recipm1_alphas_cumprod', torch.sqrt(1. / alphas_cumprod - 1))
+
+        # calculations for posterior q(x_{t-1} | x_t, x_0)
+
+        posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod)
+
+        # above: equal to 1. / (1. / (1. - alpha_cumprod_tm1) + alpha_t / beta_t)
+
+        register_buffer('posterior_variance', posterior_variance)
+
+        # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain
+
+        register_buffer('posterior_log_variance_clipped', torch.log(posterior_variance.clamp(min =1e-20)))
+        register_buffer('posterior_mean_coef1', betas * torch.sqrt(alphas_cumprod_prev) / (1. - alphas_cumprod))
+        register_buffer('posterior_mean_coef2', (1. - alphas_cumprod_prev) * torch.sqrt(alphas) / (1. - alphas_cumprod))
+
+        # calculate p2 reweighting
+
+        register_buffer('p2_loss_weight', (p2_loss_weight_k + alphas_cumprod / (1 - alphas_cumprod)) ** -p2_loss_weight_gamma)
+
+    def predict_start_from_noise(self, x_t, t, noise):
+        return (
+            extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * noise
+        )
+
+    def predict_noise_from_start(self, x_t, t, x0):
+        return (
+            (extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - x0) / \
+            extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
+        )
+
+    def predict_v(self, x_start, t, noise):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * noise -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * x_start
+        )
+
+    def predict_start_from_v(self, x_t, t, v):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_t.shape) * v
+        )
+
+    def q_posterior(self, x_start, x_t, t):
+        posterior_mean = (
+            extract(self.posterior_mean_coef1, t, x_t.shape) * x_start +
+            extract(self.posterior_mean_coef2, t, x_t.shape) * x_t
+        )
+        posterior_variance = extract(self.posterior_variance, t, x_t.shape)
+        posterior_log_variance_clipped = extract(self.posterior_log_variance_clipped, t, x_t.shape)
+        return posterior_mean, posterior_variance, posterior_log_variance_clipped
+
+    def model_predictions(self, x, t, x_self_cond = None, clip_x_start = False):
+        model_output = self.model(x, t, x_self_cond)
+        maybe_clip = partial(torch.clamp, min = -1., max = 1.) if clip_x_start else identity
+
+        if self.objective == 'pred_noise':
+            pred_noise = model_output
+            x_start = self.predict_start_from_noise(x, t, pred_noise)
+            x_start = maybe_clip(x_start)
+
+        elif self.objective == 'pred_x0':
+            x_start = model_output
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
+        elif self.objective == 'pred_v':
+            v = model_output
+            x_start = self.predict_start_from_v(x, t, v)
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
+        return ModelPrediction(pred_noise, x_start)
+
+    def p_mean_variance(self, x, t, x_self_cond = None, clip_denoised = True):
+        preds = self.model_predictions(x, t, x_self_cond)
+        x_start = preds.pred_x_start
+
+        if clip_denoised:
+            x_start.clamp_(-1., 1.)
+
+        model_mean, posterior_variance, posterior_log_variance = self.q_posterior(x_start = x_start, x_t = x, t = t)
+        return model_mean, posterior_variance, posterior_log_variance, x_start
+
+    @torch.no_grad()
+    def p_sample(self, x, t: int, x_self_cond = None, clip_denoised = True):
+        b, *_, device = *x.shape, x.device
+        batched_times = torch.full((x.shape[0],), t, device = x.device, dtype = torch.long)
+        model_mean, _, model_log_variance, x_start = self.p_mean_variance(x = x, t = batched_times, x_self_cond = x_self_cond, clip_denoised = clip_denoised)
+        noise = torch.randn_like(x) if t > 0 else 0. # no noise if t == 0
+        pred_img = model_mean + (0.5 * model_log_variance).exp() * noise
+        return pred_img, x_start
+
+    @torch.no_grad()
+    def p_sample_loop(self, shape):
+        batch, device = shape[0], self.betas.device
+
+        img = torch.randn(shape, device=device)
+
+        x_start = None
+
+        for t in tqdm(reversed(range(0, self.num_timesteps)), desc = 'sampling loop time step', total = self.num_timesteps):
+            self_cond = x_start if self.self_condition else None
+            img, x_start = self.p_sample(img, t, self_cond)
+
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def ddim_sample(self, shape, clip_denoised = True):
+        batch, device, total_timesteps, sampling_timesteps, eta, objective = shape[0], self.betas.device, self.num_timesteps, self.sampling_timesteps, self.ddim_sampling_eta, self.objective
+
+        times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1)   # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps
+        times = list(reversed(times.int().tolist()))
+        time_pairs = list(zip(times[:-1], times[1:])) # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)]
+
+        img = torch.randn(shape, device = device)
+
+        x_start = None
+
+        for time, time_next in tqdm(time_pairs, desc = 'sampling loop time step'):
+            time_cond = torch.full((batch,), time, device=device, dtype=torch.long)
+            self_cond = x_start if self.self_condition else None
+            pred_noise, x_start, *_ = self.model_predictions(img, time_cond, self_cond, clip_x_start = clip_denoised)
+
+            if time_next < 0:
+                img = x_start
+                continue
+
+            alpha = self.alphas_cumprod[time]
+            alpha_next = self.alphas_cumprod[time_next]
+
+            sigma = eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt()
+            c = (1 - alpha_next - sigma ** 2).sqrt()
+
+            noise = torch.randn_like(img)
+
+            img = x_start * alpha_next.sqrt() + \
+                  c * pred_noise + \
+                  sigma * noise
+
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def sample(self, batch_size = 16):
+        seq_length, channels = self.seq_length, self.channels
+        sample_fn = self.p_sample_loop if not self.is_ddim_sampling else self.ddim_sample
+        return sample_fn((batch_size, channels, seq_length))
+
+    @torch.no_grad()
+    def interpolate(self, x1, x2, t = None, lam = 0.5):
+        b, *_, device = *x1.shape, x1.device
+        t = default(t, self.num_timesteps - 1)
+
+        assert x1.shape == x2.shape
+
+        t_batched = torch.stack([torch.tensor(t, device = device)] * b)
+        xt1, xt2 = map(lambda x: self.q_sample(x, t = t_batched), (x1, x2))
+
+        img = (1 - lam) * xt1 + lam * xt2
+        for i in tqdm(reversed(range(0, t)), desc = 'interpolation sample time step', total = t):
+            img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))
+
+        return img
+
+    def q_sample(self, x_start, t, noise=None):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start +
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise
+        )
+
+    @property
+    def loss_fn(self):
+        if self.loss_type == 'l1':
+            return F.l1_loss
+        elif self.loss_type == 'l2':
+            return F.mse_loss
+        else:
+            raise ValueError(f'invalid loss type {self.loss_type}')
+
+    def p_losses(self, x_start, t, noise = None):
+        b, c, n = x_start.shape
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        # noise sample
+
+        x = self.q_sample(x_start = x_start, t = t, noise = noise)
+
+        # if doing self-conditioning, 50% of the time, predict x_start from current set of times
+        # and condition with unet with that
+        # this technique will slow down training by 25%, but seems to lower FID significantly
+
+        x_self_cond = None
+        if self.self_condition and random() < 0.5:
+            with torch.no_grad():
+                x_self_cond = self.model_predictions(x, t).pred_x_start
+                x_self_cond.detach_()
+
+        # predict and take gradient step
+
+        model_out = self.model(x, t, x_self_cond)
+
+        if self.objective == 'pred_noise':
+            target = noise
+        elif self.objective == 'pred_x0':
+            target = x_start
+        elif self.objective == 'pred_v':
+            v = self.predict_v(x_start, t, noise)
+            target = v
+        else:
+            raise ValueError(f'unknown objective {self.objective}')
+
+        loss = self.loss_fn(model_out, target, reduction = 'none')
+        loss = reduce(loss, 'b ... -> b (...)', 'mean')
+
+        loss = loss * extract(self.p2_loss_weight, t, loss.shape)
+        return loss.mean()
+
+    def forward(self, img, *args, **kwargs):
+        b, c, n, device, seq_length, = *img.shape, img.device, self.seq_length
+        assert n == seq_length, f'seq length must be {seq_length}'
+        t = torch.randint(0, self.num_timesteps, (b,), device=device).long()
+
+        img = normalize_to_neg_one_to_one(img)
+        return self.p_losses(img, t, *args, **kwargs)
diff --git a/setup.py b/setup.py
index 503bafd..a43d2da 100644
--- a/setup.py
+++ b/setup.py
@@ -3,7 +3,7 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.30.0',
+  version = '0.31.0',
   license='MIT',
   description = 'Denoising Diffusion Probabilistic Models - Pytorch',
   author = 'Phil Wang',