```python
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.utils.cpp_extension import load_inline


_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor conv3d_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias,
    int64_t stride,
    int64_t padding,
    int64_t dilation,
    int64_t groups);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>

template<bool CheckBounds>
__global__ __launch_bounds__(256)
void conv3d_kernel(
    const float* __restrict__ x,
    const float* __restrict__ weight,
    const float* __restrict__ bias,
    float* __restrict__ output,
    int C, int D, int H, int W,
    int OC, int KD, int KH, int KW,
    int OD, int OH, int OW,
    int stride, int padding, int dilation,
    int groups)
{
    __shared__ float a[64][33];
    __shared__ float b[32][64];

    const int tx = threadIdx.x;
    const int ty = threadIdx.y;
    const int tid = ty * 16 + tx;
    const int ic_group = C / groups;
    const int oc_group = OC / groups;
    const int channel_tiles = (oc_group + 63) / 64;
    const int group = blockIdx.y / channel_tiles;
    const int channel_base = (blockIdx.y % channel_tiles) * 64;
    const int spatial_base = blockIdx.x * 64;
    const int spatial_size = OD * OH * OW;
    const int kernel_volume = KD * KH * KW;
    const int reduction_size = ic_group * kernel_volume;
    const int batch = blockIdx.z;

    float accum[4][4];
    #pragma unroll
    for (int i = 0; i < 4; ++i)
        #pragma unroll
        for (int j = 0; j < 4; ++j)
            accum[i][j] = 0.0f;

    // Each thread loads four reduction rows at one spatial position.
    const int load_position = spatial_base + tid % 64;
    int pos = load_position;
    const int iw0 = (pos % OW) * stride - padding;
    pos /= OW;
    const int ih0 = (pos % OH) * stride - padding;
    const int id0 = (pos / OH) * stride - padding;

    for (int k0 = 0; k0 < reduction_size; k0 += 32) {
        #pragma unroll
        for (int t = 0; t < 8; ++t) {
            const int index = tid + t * 256;
            const int row = index / 32;
            const int col = index % 32;
            const int oc = channel_base + row;
            const int k = k0 + col;

            float value = 0.0f;
            if (oc < oc_group && k < reduction_size) {
                const int global_oc = group * oc_group + oc;
                value = weight[
                    static_cast<int64_t>(global_oc) * reduction_size + k];
            }
            a[row][col] = value;
        }

        #pragma unroll
        for (int t = 0; t < 8; ++t) {
            const int row = tid / 64 + t * 4;
            const int col = tid % 64;
            const int k = k0 + row;
            float value = 0.0f;

            if (k < reduction_size && load_position < spatial_size) {
                int q = k;
                const int kw = q % KW;
                q /= KW;
                const int kh = q % KH;
                q /= KH;
                const int kd = q % KD;
                const int ic = q / KD;

                const int iz = id0 + kd * dilation;
                const int iy = ih0 + kh * dilation;
                const int ix = iw0 + kw * dilation;

                if (!CheckBounds ||
                    (static_cast<unsigned>(iz) < static_cast<unsigned>(D) &&
                     static_cast<unsigned>(iy) < static_cast<unsigned>(H) &&
                     static_cast<unsigned>(ix) < static_cast<unsigned>(W))) {
                    const int global_ic = group * ic_group + ic;
                    const int64_t offset =
                        (((static_cast<int64_t>(batch) * C + global_ic)
                           * D + iz) * H + iy) * W + ix;
                    value = x[offset];
                }
            }
            b[row][col] = value;
        }
        __syncthreads();

        #pragma unroll
        for (int k = 0; k < 32; ++k) {
            float av[4];
            float bv[4];

            #pragma unroll
            for (int i = 0; i < 4; ++i)
                av[i] = a[ty + i * 16][k];

            #pragma unroll
            for (int j = 0; j < 4; ++j)
                bv[j] = b[k][tx + j * 16];

            #pragma unroll
            for (int i = 0; i < 4; ++i)
                #pragma unroll
                for (int j = 0; j < 4; ++j)
                    accum[i][j] = fmaf(av[i], bv[j], accum[i][j]);
        }
        __syncthreads();
    }

    #pragma unroll
    for (int i = 0; i < 4; ++i) {
        const int oc = channel_base + ty + i * 16;
        if (oc < oc_group) {
            const int global_oc = group * oc_group + oc;
            const float bias_value = bias ? bias[global_oc] : 0.0f;
            const int64_t base =
                (static_cast<int64_t>(batch) * OC + global_oc) * spatial_size;

            #pragma unroll
            for (int j = 0; j < 4; ++j) {
                const int spatial = spatial_base + tx + j * 16;
                if (spatial < spatial_size)
                    output[base + spatial] = accum[i][j] + bias_value;
            }
        }
    }
}

torch::Tensor conv3d_cuda(
    torch::Tensor x,
    torch::Tensor weight,
    c10::optional<torch::Tensor> bias,
    int64_t stride,
    int64_t padding,
    int64_t dilation,
    int64_t groups)
{
    const c10::cuda::CUDAGuard device_guard(x.device());

    TORCH_CHECK(x.is_cuda() && weight.is_cuda(), "Expected CUDA tensors");
    TORCH_CHECK(x.scalar_type() == at::kFloat &&
                weight.scalar_type() == at::kFloat, "Expected float32 tensors");
    TORCH_CHECK(x.is_contiguous() && weight.is_contiguous(),
                "Expected contiguous tensors");
    TORCH_CHECK(x.dim() == 5 && weight.dim() == 5, "Expected 5D tensors");
    TORCH_CHECK(x.device() == weight.device(), "Device mismatch");
    TORCH_CHECK(stride > 0 && dilation > 0 && padding >= 0 && groups > 0,
                "Invalid convolution parameters");

    const int N = x.size(0);
    const int C = x.size(1);
    const int D = x.size(2);
    const int H = x.size(3);
    const int W = x.size(4);
    const int OC = weight.size(0);
    const int KD = weight.size(2);
    const int KH = weight.size(3);
    const int KW = weight.size(4);

    TORCH_CHECK(C == weight.size(1) * groups && OC % groups == 0,
                "Invalid channel dimensions");

    const int64_t dz = D + 2 * padding - dilation * (KD - 1) - 1;
    const int64_t dy = H + 2 * padding - dilation * (KH - 1) - 1;
    const int64_t dx = W + 2 * padding - dilation * (KW - 1) - 1;
    TORCH_CHECK(dz >= 0 && dy >= 0 && dx >= 0,
                "Kernel exceeds padded input");

    const int OD = dz / stride + 1;
    const int OH = dy / stride + 1;
    const int OW = dx / stride + 1;

    auto output = torch::empty({N, OC, OD, OH, OW}, x.options());
    if (output.numel() == 0)
        return output;

    const float* bias_ptr = nullptr;
    if (bias.has_value()) {
        TORCH_CHECK(bias->device() == x.device() &&
                    bias->scalar_type() == at::kFloat &&
                    bias->is_contiguous() && bias->numel() == OC,
                    "Invalid bias");
        bias_ptr = bias->data_ptr<float>();
    }

    const dim3 block(16, 16);
    const dim3 grid(
        (OD * OH * OW + 63) / 64,
        ((OC / groups + 63) / 64) * groups,
        N);
    const auto stream = at::cuda::getCurrentCUDAStream();

    if (padding == 0) {
        conv3d_kernel<false><<<grid, block, 0, stream>>>(
            x.data_ptr<float>(), weight.data_ptr<float>(), bias_ptr,
            output.data_ptr<float>(),
            C, D, H, W, OC, KD, KH, KW, OD, OH, OW,
            stride, padding, dilation, groups);
    } else {
        conv3d_kernel<true><<<grid, block, 0, stream>>>(
            x.data_ptr<float>(), weight.data_ptr<float>(), bias_ptr,
            output.data_ptr<float>(),
            C, D, H, W, OC, KD, KH, KW, OD, OH, OW,
            stride, padding, dilation, groups);
    }
    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_extension = load_inline(
    name="tiled_implicit_conv3d_f32",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["conv3d_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class _Conv3dFunction(torch.autograd.Function):
    @staticmethod
    def forward(ctx, x, weight, bias, stride, padding, dilation, groups):
        ctx.save_for_backward(x, weight)
        ctx.params = (stride, padding, dilation, groups)
        ctx.has_bias = bias is not None
        return _extension.conv3d_cuda(
            x.contiguous(),
            weight.contiguous(),
            None if bias is None else bias.contiguous(),
            stride,
            padding,
            dilation,
            groups,
        )

    @staticmethod
    def backward(ctx, grad_output):
        x, weight = ctx.saved_tensors
        stride, padding, dilation, groups = ctx.params
        grad_output = grad_output.contiguous()

        grad_x = grad_weight = grad_bias = None
        if ctx.needs_input_grad[0]:
            grad_x = torch.nn.grad.conv3d_input(
                x.shape, weight, grad_output,
                stride, padding, dilation, groups,
            )
        if ctx.needs_input_grad[1]:
            grad_weight = torch.nn.grad.conv3d_weight(
                x, weight.shape, grad_output,
                stride, padding, dilation, groups,
            )
        if ctx.has_bias and ctx.needs_input_grad[2]:
            grad_bias = grad_output.sum(dim=(0, 2, 3, 4))
        return grad_x, grad_weight, grad_bias, None, None, None, None


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels: int,
        out_channels: int,
        kernel_size: int,
        stride: int = 1,
        padding: int = 0,
        dilation: int = 1,
        groups: int = 1,
        bias: bool = False,
    ):
        super().__init__()
        self.conv3d = nn.Conv3d(
            in_channels,
            out_channels,
            (kernel_size, kernel_size, kernel_size),
            stride=stride,
            padding=padding,
            dilation=dilation,
            groups=groups,
            bias=bias,
        )

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        conv = self.conv3d
        scalar_parameters = (
            len(set(conv.stride)) == 1
            and isinstance(conv.padding, tuple)
            and len(set(conv.padding)) == 1
            and len(set(conv.dilation)) == 1
        )
        if (
            not x.is_cuda
            or x.dtype != torch.float32
            or conv.weight.dtype != torch.float32
            or x.dim() != 5
            or not scalar_parameters
            or torch.is_autocast_enabled()
        ):
            return conv(x)

        return _Conv3dFunction.apply(
            x,
            conv.weight,
            conv.bias,
            conv.stride[0],
            conv.padding[0],
            conv.dilation[0],
            conv.groups,
        )
```